The following 19 questions cover some of the material that is relevant for the second exam.
The exact questions given below will not be on the exam. Questions that are similar to (at least) some of them will be. Understanding the answers to these questions will therefore help you prepare for the exam.
Answers and explanations for all 19 questions are found at the bottom of this page. The link after each question takes you to the relevant answer. Please note that while checking the answer to question 3 (for example), you may also be able to see the answer to question 4. If you prefer not to see an answer before you've read the corresponding question, you may wish to look over all the questions before checking any answers.
Please note that studying for the second exam should entail more than merely reviewing this page. The exam itself has 17 questions, and while these questions cover much of what we've done in class, there will almost certainly be topics appearing on the exam that do not appear in these sample questions. Make sure to also study your class notes and the homework questions. Finally, note that you do not receive any direct credit for accessing this page, nor is the page set up to report a score based on your answers.
| Quantity | Price | Total Revenue |
|---|---|---|
| 1 | 60 | 60 |
| 2 | 57 | 114 |
| 3 | 54 | 162 |
| 4 | 51 | 204 |
| 5 | 48 | 240 |
| 6 | 45 | 270 |
| 7 | 42 | 294 |
| 8 | 39 | 312 |
| Willingness To Pay | |||
|---|---|---|---|
| Person A | Person B | Marginal Cost |
|
| high-quality (H) | 16 | 10 | 5 |
| low-quality (L) | 10 | 7 | 2 |
The firm wishes to establish prices at which the two customers
buy different types of the good (i.e., at which the customers
``self select''). At part of this strategy, the firm sets its price
for the low-quality good at PL = $7. Complete the
following. The highest price that the firm can charge for the
high-quality good and still have the customers self select is
PH = _____.
[answer and explanation]
Each of the accompanying tables describes one set of payoffs the firms could receive. The lower, left-hand number in each square represents Firm 1's payoff; the upper, right-hand number represents Firm 2's payoff (a higher number is better for a firm than is a lower number). [Assume the firms interact just one time, that the firms choose their actions simultaneously, and that the firms can't sign binding contracts.]
(I apologize for the rather goofy looking tables, but it's the best I'm going to do.)
| Game I | Game II | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Firm 2 | Firm 2 | |||||||||||||||
| price high | price low | price high | price low | |||||||||||||
| Firm 1 | price high | 20 | 25 | Firm 1 | price high | 20 | 25 | |||||||||
| 20 | 15 | 20 | 10 | |||||||||||||
| price low | 15 | 10 | price low | 10 | 15 | |||||||||||
| 25 | 10 | 25 | 15 | |||||||||||||
Based on the payoffs described in the tables, complete the
following statement about the situation facing Firm 1. In
Game I, Firm 1 has _____; in Game II, Firm 1 has _____.
[answer and explanation]
Each of the accompanying tables describes one set of payoffs the players could receive. Each player's payoffs are shown in the standard location, and higher payoffs are better.
| Game I | Game II | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Player 2 | Player 2 | |||||||||||||||
| Orange | Blue | Orange | Blue | |||||||||||||
| Player 1 | Red | 14 | 28 | Player 1 | Red | 12 | 24 | |||||||||
| 30 | 12 | 10 | 20 | |||||||||||||
| Black | 20 | 22 | Black | 18 | 16 | |||||||||||
| 18 | 24 | 22 | 14 | |||||||||||||
Complete the following by inserting the number of equilibria that
exist in each game. Game I: ____; Game II: _____.
[answer and explanation]
| Sam | |||||||
|---|---|---|---|---|---|---|---|
| quiet | cheer | ||||||
| Me | quiet | 0 | 2 | ||||
| 0 | 1 | cheer | 1 | 3 | |||
| 2 | 3 | ||||||
| Player B | |||||||
|---|---|---|---|---|---|---|---|
| c'op'ate | defect | ||||||
| Player A | cooperate | 4 | 5 | ||||
| 4 | 2 | defect | 2 | x | |||
| 5 | x | ||||||
American and Japanese ships were the first to exploit it. Now fleets of Mexican fisherman, mostly unlicensed and ungoverned, are taking whatever they can, as fast as they can, for the American and Asian markets. Every important species of fish in the sea is in sharp decline, fishermen and marine scientists say. ... "The philosophy is: get it now; grab it -- if I don't, the next guy will," said Juan Pablo Gallo, a marine biologist in Guanmas.
Question 1 answer is: b. price-taker firm ; price-setter firm
Explanation: A price taker is a firm that has no control over the price at which it sells its product. Such a firm must simply take the market price as a given and respond by deciding how many units to sell. Now matter how a price-taking firm changes the quantity that it produces, the price at which it sells its product does not change.
In this question, Firm A can increase its production from 2000 to 4000 units without there being any change in the $200 price it gets for its product. Firm A therefore faces a horizontal firm demand curve, and is a price taker.
A price setter is a firm one that has some ability to choose the price at which it sells its product. The firm knows that it picks a higher price, it will sell fewer units; if it wants to increase the quantity it sells, it knows (other things -- such as advertising, product quality, etc. -- held constant) that it must lower its price.
In this question, when Firm B increases its production from 2000 to 4000 units, it can sell that increased quantity only by reducing its selling price from $200 to $150. In other words, Firm B faces a downward-sloping firm demand curve. Firm B therefore is a price setter.
Generally speaking, we'd expect that a price-taking firm is one that is small relative to the size of its market (like a single wheat farmer), while a price-setting firm makes up a bigger share the market for its product. In the question, both Firm A and Firm B are originally producing 2000 units, and then increase their production to 4000 units. This does not, however, mean that both firms are the same size relative to the sizes of their markets. In fact, Firm A's 4000 units might be a tiny share of the market for its product, while B's 4000 units might be a larger share of the market for its (different) product.
Finally, note that in this question it seems like it might be better to be Firm A than to be Firm B (since A can increase its sales without having to accept a lower price). Bear in mind, however, that since Firm B faces a downward-sloping demand curve, it has an opportunity that Firm A doesn't have; namely, it can choose to raise its price while knowing that so doing will cost it only some (but not all) of its sales.
Question 2 answer is: d. $20
Explanation: One way to answer this question is to simply plug numbers into the formula for Marginal Revenue given in class. That formula shows that selling an additional unit affects the firm's revenue in two ways. First, the firm's gain in revenue equals the price at which it sells the new unit. In order to sell that unit, however, the firm had to reduce its selling price, which means that the firm collects less on all the sales it would have made anyway (without the price reduction).
The Marginal Revenue formula illustrates these two effects, According to the formula, Linda's Marginal Revenue from selling a 20th unit is expressed as:
Note that the numbers on the right-hand side of the formula depend on the number on the left-hand side. For example, the MR from selling unit 21 = (P at which 21th was sold) - (20) (drop in price needed to sell the 21st unit). In this problem, of course, the "drop in price needed to sell" the 20th unit is $2.
[While it's not relevant to this question, also note the following. If a firm can sell more units without having to decrease its price in order to do so, the "drop in price" term in the above formula is zero. The formula then tells us that Marginal Revenue equals Price. This is the case of a "price taker" firm that can sell as much as it wants without needing to lower its price in order to do so.]
Plugging in the numbers from the problem, we see that the MR from selling the 20th unit = $58 - (19 × $2) = $58 - $38 = $20. [Remember the "order of operations" -- do the multiplication before doing the subtraction.]
The alternate way to answer this question is to find Linda's Total Revenue when she sells 19 units (at a price of $60 each) and her TR when she sells 20 (at a price of $58 each (since she had to lower her price by $2 in order to make the 20th sale)). Linda's Marginal Revenue from selling the 20th unit is the difference between these two figures.
In this example, Total Revenue when 19 units are sold is TR = 19 × $60 = $1140, and TR when 20 units are sold is TR = 20 × $58 = $1160. Clearly, selling the 20th unit increases Linda's Total Revenue by $20; her Marginal Revenue from selling the 20th unit is therefore $20.
Question 3 answer is: e. both answers (b) -- decrease this firm's profit -- and (c) -- produce a net benefit for society; in other words, be efficient -- are correct.
Explanation: First, we need to compare the Marginal Revenue from selling the 9th unit with the Marginal Cost of producing it. The formula for Marginal Revenue says that
In this case, the MR from selling the 9th unit = 9.50 - 8 × (.50) = 5.50.
We can now compare Marginal Revenue (= $5.50) and Marginal Cost (= $7). Since MR is less than MC, we know that increasing sales from 8 units to 9 units will decrease the firm's profit (since the firm's revenue will rise by a smaller amount than its cost will rise).
Now, consider the "net benefit" part of the question. To answer this, we need to compare the value that a consumer places on the 9th unit with the cost of producing it. In this question, somebody would be willing to pay ($10 minus 50 cents =) $9.50 to buy the 9th unit. This tells us that the person who buys the 9th unit of the good must get $9.50 worth of value from consuming it. The marginal cost of producing that unit is only $7.
We conclude that producing and selling the 9th unit of the good would produce an increase in efficiency (would raise Total Surplus) for the overall society because the value that the customer would get from consuming that unit of the good exceeds the cost of producing it.
The fact that the firm will choose not to produce and sell the 9th unit (because doing so would lower its profit), even though selling that unit would raise economic efficiency, tells us that this firm chooses to produce less than the efficient quantity of this good. This conclusion is, of course, consistent with what we've said about the output decisions made by monopoly firms.
Question 4 answer is: b. 51
Explanation: Like question 7, the simplest way to start solving this problem is probably to convert the information in it into the form of Marginal Revenue and Marginal Cost.
| Quantity | Total Revenue |
Marginal Revenue | Marginal Cost |
|---|---|---|---|
| 1 | 60 | 60 | 40 |
| 2 | 114 | 54 | 40 |
| 3 | 162 | 48 | 40 |
| 4 | 204 | 42 | 40 |
| 5 | 240 | 36 | 40 |
| 6 | 270 | 30 | 40 |
| 7 | 294 | 24 | 40 |
| 8 | 312 | 18 | 40 |
In this problem, the simplest way to find Marginal Revenue is to look at how selling one additional unit changes Total Revenue. The Marginal Revenue of the 2nd unit, for example, is the change between TR when 2 units are sold and TR when 3 units are sold.
Marginal Cost is simply given in the question, which states that MC = 40.
A firm that wants to maximize its profit should sell all units for which Marginal Revenue exceeds Marginal Cost (since selling that unit will raise its profit), and should not sell any unit for which MR is less than MC (since selling that unit will reduce its profit).
Applying this rule tells us that this firm maximizes its profit by selling 4 units. Returning to the question's original table, we see that if the firm wishes to sell 4 units, it should set its per-unit price at 51.
[You may want to review the "note" at the end of the answer to question 11.]
Question 5 answer is: d. rise ; fall ; rise
Explanation: Starting from the monopoly-firm outcome, a rise in the quantity produced will cause the market price to fall. Since consumers will be buying more units at a lower price, their Consumer Surplus will rise.
Since the monopoly outcome is the one that maximizes Profit (or Producer Surplus), any movement away from that outcome -- in this case, an increase in output -- must reduce Producer Surplus.
The remaining question is whether or not the rise in Consumer Surplus and the fall in Producer Surplus offset each other, leaving Total Surplus unchanged. They do not. Remember that the monopoly outcome is inefficient, because the quantity produced is ``too small''. [In order to make positive profits, the monopoly firm restricts its production.] An increase in production would move the outcome closer to the efficient outcome (which is the one that maximizes Total Surplus). [In a "properly-functioning" competitive market, TS is maximized at the market-equilibrium output, which exceeds the monopoly output.]
If you draw the pictures for a monopoly market, you'll see that a rise in quantity helps consumers by more than it hurts producers, and causes Total Surplus to rise.
Question 6 answer is: c. does ; doesn't currently ; consumers
Explanation: For a product that already exists, a profit-seeking monopoly will charge a Price above its Marginal Cost of production. As a result, it will sell an inefficently small quantity of the good. [In other words, it will stop producing the item before the point at which consumer Value for the good equals the Marginal Cost of producing it.] In contrast, when a (potential) product hasn't yet been discovered, the profits that might be available to a monopoiy firm could be the motivation needed to get some firm (or some person) to be willing to incur the expense needed to discover and develop the product.
The key phrase in this question is that "new firms are always able to enter" to market. When there's a reduction in the cost of producing a good, the firms producing it experience a rise in their profits. In order to get a share (or a bigger share) of those profits, new firms will enter the market (or existing firms will exapnd). This entry (and expansion) increases market supply and reduces the equilibrium market price. The positive profits that firms earned in the short run will disappear as time passes. As long as entry can't be blocked, the long-run outcome in a market system is that a rise in productivity most benefits the consumers of the good who gain from the lower market price.
Question 7 answer is: e. None of (i), (ii), and (iii) is true.
Explanation: A monopolistically-competitive market has some features that are like those (and some unlike those) in a perfectly-competitive market, and some features that are like those (and some unlike those) in a monopoly market.
Firms in a perfectly-competitive market do have perfectly-horizontal firm demand curves. This is because perfectly-competitive firms are price takers; in other words, they can sell any quantity of output at the market price. Monopolistically-competitive firms, however, have some degree of market power, which implies that they can choose their selling price. Of course, such firms know that a higher price will lead to a drop in sales (but sales won't fall immediately to zero). In other words, monopolistically-competitive firms have downward-sloping firm demand curves. Statement (i) is thus not correct.
In a true monopoly, new firms are unable to enter the market. The existing firm can thus continue to earn monopoly profits. In a monopolistically-competitive market, however, it is possible for firms to enter the market, and these new firms will cause the profits of the existing firms to fall. Statement (ii) is thus not correct.
In a perfectly-competitive market, costs are indeed driven down to their lowest possible level (the minimum point of the Average Total Cost curve). In a monopolistically-competitive market, however, the long-run equilibrium exists when the firm demand curve is just tangent to the ATC curve (this is the condition for there to be zero economic profit). Since the firm demand curve is downward-sloping, this tangency must occur on the downward-sloping part (rather than at the minimum point) of the ATC curve. In other words, when the market is in long-run equilibrium, Average Total Cost is not as low as it could possibly be. Statement (iii) is thus not correct.
[The previous point is related to the variety-vs.-cost tradeoff covered in class. Start from the long-run equilibrium in a monopolistically-competitive market. If a firm raised its quantity of production, it would move down its ATC curve; as the firm grew, therefore, its average cost of production would fall. However, as some firms grow, others must disappear from the market. Thus, the long-run equilibrium outcome involves more variety, but higher costs of production; an outcome with a smaller number of bigger firms would have less variety (which is bad), but also lower production costs (which is good).]
Question 8 answer is: a. a higher price in Market A
Explanation: This is a question about price differentiation, which exists when a firm charges different customers different prices for the "same" good. In this question, customers are differentiated by the value of the elasticity of their demand curves.
Remember that the larger the value of the demand elasticity, the larger the reduction in the quantity demanded when the price rises. A firm is better off, therefore, with a lower value for the elasticity -- the smaller the elasticity, the smaller the loss in sales when the firm raises its price. A firm selling to a group of customers that has a lower demand elasticity will therefore find it profitable to charge a higher price. In contrast, a firm selling to a group of customers with a larger demand elasticity will be forced to charge a lower price (since a high price would lead to a big drop in sales).
In this question, the elasticity in Market A is 3; this is the "smaller" elasticity, so the firm should charge a higher price in Market A. The elasticity in Market B is 5; this is the "larger" elasticity, so the firm should charge a lower price in Market B.
While it isn't needed for this question, we could in fact produce a more specific answer. The question gives the elasticities in the two markets. Let's suppose that we also know the Marginal Cost of production; let's say that MC equals $10.
Remember the following formula that we developed in class:
|
If we plug Elas = 3, and MC = 10 into the last formula, we get Price = (3/2) × 10 = $15. Plugging in Elas = 5 produces Price = (5/4) × 10 = $12.50. A higher price ($15) is indeed charged in the market with the lower elasticity (3), while a lower price ($12.50) is charged in the market with the higher elasticity (5).
Question 9 answer is: b. $13
Explanation: First, the question asks about "hav[ing] the customers self select". This means simply that the firm wants to pick prices for the high- and low-quality versions of its product that lead Person A (who values high quality relatively more than does Person B) to buy the highr-quality version, and Person B to buy the low-quality version. By behaving in this way, the customers "self select" themselves into different groups. The firm's desire to achieve this outcome is motivated by the fact that it can often earn a larger profit by selling two (or more) versions of its product at different prices (and thus practicing price differentiation) than it can earn by selling only a single version at a single price.
The question states that the low-quality version of this product is sold at a price of PL = $7. [The firm picked this price so that it could earn as large a profit as possible from selling to Person B.] Person A is able, if she so chooses, to buy this item. If she does so, she'll experience $3 worth of surplus (since she'll be spending $7 to buy an item for which she would have been willing to pay $10).
If the firm wishes to get Person A to buy the high-quality version instead, it must make sure that she gets (at least) $3 of surplus from buying H. [If Person A doesn't get that much surplus from buying H, she'll simply buy L instead. In this case, both Person A and Person B would buy L -- they wouldn't be self selecting.] To do this, the firm can charge no more for version H than PH = $13.
Question 10 answer is: c. no dominant strategy ; a dominant strategy -- it is to always choose "price low"
Explanation: One of the actions available to a player is a "dominant strategy" if it always gives that player a higher individual payoff (or at least as high a payoff) than does any of his other possible strategies regardless of what the other player chooses to do.
[Remember that we are talking about a noncooperative game in which each player chooses only its own action. In other words, we are looking at how one player chooses its action (and the payoff that one player gets as a result) holding constant the action of the other player. We are not considering a case in which the two players can coordinate and choose their actions as a "team."]
In the simple situation described in the question (game played just one time, each firm chooses its action before observing what the other firm does), Firm 1 has only two possible strategies -- charge a "low price" or charge a "high price."
The way to check whether Firm 1 has a dominant strategy is to find its "best response" to each of Firm 2's possible actions. We do this by first assuming that Firm 2 chooses a "high" price, and then seeing what price Firm 1 should choose in order to get itself the highest possible payoff. After this is done, then assume that Firm 2 chooses a "low" price, and again see which price offers a Firm 1 the highest payoff. If the same choice is best for Firm 1 in both situations, then that choice must be Firm 1's dominant strategy.
For Game I, begin by assuming that Firm 2 chooses "high;" in this case, Firm 1 gets a payoff of 20 if chooses "high" and a payoff of 25 if it chooses "low." [These are the two numbers that show Firm 1's two possible payoffs given that Firm 2 has chosen "high."] Obviously, Firm 1 does best in this situation by choosing "low." To indicate that "low" is Firm 1's best response to Firm 2 picking "high," we can "circle" the 25 that Firm 1 receives in this case. [In the table shown below, the 25 is bold-faced rather than circled.]
Now assume that Firm 2 chooses "low;" in this case, Firm 1 does best by choosing "high" ("high" gives Firm 1 a payoff of 15, while "low" would give Firm 1 only 10). Again, this can be shown by circling (bold-facing) the appropriate 15.
| Game I | Game II | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Firm 2 | Firm 2 | |||||||||||||||
| price high | price low | price high | price low | |||||||||||||
| Firm 1 | price high | 20 | 25 | Firm 1 | price high | 20 | 25 | |||||||||
| 20 | 15 | 20 | 10 | |||||||||||||
| price low | 15 | 10 | price low | 10 | 15 | |||||||||||
| 25 | 10 | 25 | 15 | |||||||||||||
Our results indicate that Firm 1 has no dominant strategy in Game I. If Firm 1 knows that Firm 2 will price "high," Firm 1 prefers to price "low;" if it1 knows that Firm 2 will price "low," Firm 1 prefers to price "high." In other words, Firm 1's preferred choice depends on what Firm 2 does -- there is no action that is always (individually) best for Firm 1.
Saying that Firm 1 does not have an action that is always best is equivalent to saying that it doesn't have a dominant strategy.
For Game II, follow the same procedure. Assuming first that Firm 2 chooses "high," Firm 1 does best by choosing "low" (Firm 1 gets 25 rather than the 20 it would get it if it picked "high"). Assuming next that Firm 2 chooses "low," Firm 1 again does best by choosing "low" (Firm 1 gets 15 rather than 10).
In this game, therefore, we conclude that Firm 1 does have one action is always best for itself. No matter what Firm 2 does, Firm 1 always does better individually (holding constant Firm 2's action) by pricing "low" than it does by pricing "high." Holding constant Firm 2's action, therefore, we see that pricing "low" is always the best action for Firm 1. We thus say that pricing "low" is Firm 1's dominant strategy.
Question 11 answer is: a. 1 ; 2
Explanation: For this type of game -- a simultaneous, one-time, noncooperative game -- the technique for finding an equilibrium is to (i) put yourself in the "shoes" of one player, (ii) assume that the other player takes a particular action, (iii) find the action that gives you the best payoff given what you've assumed about the other player, and circle the payoff you receive in this case, (iv) assume the other player takes a different action, (v) find the action that gives you the best payoff (and circle that payoff) given what you've now assumed about the other player, and (vi) repeat if necessary.
For Game I, in particular, first assume you are Player 1, and assume Player 2 will call "Orange." Given this assumption, the only two possible outcomes are "Red-Orange," in which you (as Player 1) get a 30, and "Black-Orange," in which you get an 18. Thus, if Player 2 is calling "Orange," Player 1 does best by calling "Red." To show this, you circle Player 1's payoff in the "Red-Orange" box (i.e., circle the 30).
Now, assume Player 2 will call "Blue." You (as Player 1) compare the 12 you'd get by choosing "Red" with the 24 you'd get by choosing "Black." Clearly, if Player 2 is choosing "Blue," Player 1 does better by choosing "Black." Show this by circling the 24 in the "Black-Blue" box.
Now, put yourself in the shoes of Player 2. If Player 1 chooses "Red," the two possible outcomes are "Red-Orange" (in which Player 2 gets a 14) and "Red-Blue" (in which Player 2 gets 28). Clearly, if Player 1 chooses "Red", Player 2 does best by choosing "Blue." Show this by circling Player 2's payoff (28) in the "Red-Blue" box.
Finally, assume Player 1 chooses "Black." Player 2 does better by choosing "Blue" (and getting 22) than by choosing "Orange" (and getting 20). Circle the 22 in the "Black-Blue" box.
The game tables are reproduced here, using bold face rather than circles to illustrate the best action for each player, assuming a particular action for its opponent.
| Game I | Game II | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Player 2 | Player 2 | |||||||||||||||
| Orange | Blue | Orange | Blue | |||||||||||||
| Player 1 | Red | 14 | 28 | Player | Red | 12 | 24 | |||||||||
| 30 | 12 | 10 | 20 | |||||||||||||
| Black | 20 | 22 | Black | 18 | 16 | |||||||||||
| 18 | 24 | 22 | 14 | |||||||||||||
An equilibrium exists when there are two circled (bold-faced) numbers in the same square of the table. The economic significance of this is that each player is taking the action that is best for itself, given what the other player is doing. This means that neither player can help itself by altering its action -- which is the characteristic needed for outcome to be an equilibrium.
As you can see, in Game I, there is one square with two circles -- the square in which Player 1 calls "Black" and Player 2 calls "Blue."
Let's check that this outcome is really an equilibrium. Given that Player 2 is calling "Blue," Player 1 would hurt itself by switching its call from "Black" to "Red" (its payoff would fall from 24 to 12). Also, given that Player 1 is calling "Black," Player 2 would hurt itself by switching its call from "Blue" to "Orange" (its payoff would fall from 22 to 20). Thus, neither player wants to switch away from the "Black"-"Blue" result. This means that "Black"-"Blue" is an equilibrium. Furthermore, it is the only equilibrium in Game I since there are no other squares in the game for which this is true.
While the full explanation isn't provided here (I'll let you check this -- and you should), the circles (bold-faces) have also been put into Game II. This game has two equilibria -- the "Black"-"Orange" outcome and the "Red"-"Blue" outcome. In each case, each player is choosing its best action against the action used by its opponent.
One last note. In analyzing games of this type, it is very important to compare the correct (two) payoffs. If you are pretending to be Player 1, make sure you compare Player 1's payoffs in the two squares that are possible outcomes given what you have assumed about Player 2's action. Similarly, if you are pretending to be Player 2, make sure you compare the two payoffs that are possible for Player 2, given what you have assumed about Player 1.
Question 12 answer is: b. A "prisoners' dilemma" game has both characteristics; a "chicken" game has only characteristic I.
Explanation: First, remember that both "prisoners' dilemma" and "chicken" are noncooperative games in which the players pick their actions separately -- a player has no control over the action of the other player.
Characteristic I talks about an outcome in which both players are worse off than they are in some other outcome. In other words, it refers to an outcome that is mutually-harmful for both players. This sort of outcome arises in both games.
In a "prisoners' dilemma" game, a player chooses between "cooperate" and "defect, and the payoffs are such that both players are worse off in the "defect"-"defect" outcome than they are in the "cooperate"-"cooperate" outcome.
In a "chicken" game, a player chooses between "swerve" (or "give in") and "not swerve" (or be "tough"), and the payoffs are such that both players are worse off in the "not swerve"-"not swerve" outcome than they are in the "swerve"-"swerve" outcome.
Characteristic II states that the mutually-harmful outcome described in (I) in an equilibrium of the game. A game is in an equilibrium outcome when each player is using his or her best response to what the other player is doing.
In a Prisoners' Dilemma, the mutually-harmful "defect"-"defect" outcome arises when each player uses his or her Dominant Stratgey (which is to "defect"). [A player has a Dominant Strategy when one of his possible actions always leaves him better off than would his other possible action (holding constant the choice of the other player. In a one-time Prisoners' Dilemma a player always gets a higher personal payoff by choosing to "defect" than he gets by choosing to "cooperate" regardless of what the other player does.] In a one-time Prisoners' Dilemma, a player could never help herself by switching from "defect" to "cooperate". The "defect"-"defect" outcome therefore is an equilibrium of a one-time Prisoners' Dilemma (because neither player can gain by changing just her own action).
In a Chicken Game, however, the mutually-harmful "tough"-"tough" outcome is one that players might find themselves in accidentally. This could happen if each player commits to being "tough" in hopes of getting the other player to "give in". [Such a commitment strategy can work well if only one player uses it, and the other really does give in.] If the players found themselves in the "tough"-"tough" outcome, however, either one would wish that he had picked a different action -- when the other player is "tough", a player is better off "giving in" than also being "tough". In a Chicken Game, the "tough"-"tough" outcome is thus not an equilibrium because either player could have helped himself by changing only his own action.
[By the way, Game II in Question 10 is a game in which the payoffs have the pattern of a prisoner's dilemma. In this case, to "price low" is to "defect." Given whatever action is chosen by Firm 2, Firm 1 can always increase its own payoff by choosing "low" (and the same is true for Firm 2). When both firms choose "low," however, they both end up worse off than if both had picked "high."]
Question 13 answer is: d. neither a Prisoners' Dilemma nor a Chicken Game
The "game" between Sam and I has one of the characteristics of a Prisoners' Dilemma; namely, each player has a dominant strategy. No matter what Sam does, my payoff is higher if I choose to "cheer" than it is if I choose to be "quiet". [Sam's dominant strategy is also to "cheer".]
For a game to be called a Prisoners' Dilemma, though, there must be a "dilemma" -- there must be a conflict between doing something that helps yourself and doing something that is beneficial for the overall group. In a Prisoners' Dilemma, if each player tries to help him- or herself, all the players end up worse off than they would have been if they had chosen some other action.
That sort of conflict does not exist in this game. When Sam and I each help ourselves by "cheer"ing, we also help the other person -- the outcome in which we both "cheer" is the best-possible outcome for both of us. The fact that helping yourself also helps the group means that this situation does not qualify as a Prisoners' Dilemma.
It also does not qualify as a Chicken Game. There are several reasons for this. One is that each player has a dominant strategy; a player in a Chicken Game doesn't. Another reason is that there is only one equilibrium in this game (in which both "cheer"); a Chicken Game has two equilibria.
So, if this game is neither a Prisoners' Dilemma nor a Chicken Game, what is it? It's "game" that we haven't studied in this class; you won't be asked to try to "name" it. [We didn't study this game for a good reason -- from a strategic viewpoint, it isn't very interesting. We can confidently predict that both players will cheer, and will be happy doing so.]
Question 14 answer is: c. a number between 2 and 4
Explanation: The prisoners' dilemma is called a "dilemma" because a person involved in such a game faces a conflict between taking one action that is always beneficial to him- or herself individually (in other words, is a dominant strategy), or taking another action that (if everybody did the same) would be beneficial for the group.
| Player B | |||||||
|---|---|---|---|---|---|---|---|
| c'op'ate | cheat | ||||||
| Player A | cooperate | 4 | 5 | ||||
| 4 | 2 | cheat | 2 | 3 | |||
| 5 | 3 | ||||||
In this game, if Player B "cooperates", then Player A can get either a payoff of 4 (by choosing to "cooperate") or a payoff of 5 (by choosing to "cheat"). In this case, "cheat" clearly produces a higher payoff. For "cheat" to be a dominant strategy it must, holding constant Player B's action, always yield a higher payoff than does "cooperate" Thus, the x in this game must be a number bigger than 2, so that when Player B picks "cheat", Player A again does better by picking "cheat" than by picking "cooperate".
The existence of a dominant strategy, however, is not the end of the story. For a game to be a prisoners' dilemma, it must be true that when both players use their dominant strategy, they both end up with a lower payoff than they would experience had they both chosen the more cooperative action. Thus, the x in this game must be a smaller number than the "4" that appears in the "cooperate"-"cooperate" box.
Obviously, if x must be greater than 2 and less than 4, one possible value for x is 3. As shown in the accompanying table, such a value creates the pattern of incentives associated with a prisoners' dilemma.
Question 15 answer is: a. defect ; cooperate ; defect-defect
Explanation: Two key elements of a Prisoners' Dilemma are: (i) there's one action available to a player that always leaves him or her (at least in the short run) individually better off (holding constant the actions of the other players), but (ii) if every player tries to help him- or herself individually, each of them ends up personally worse off than he or she would have been in a different outcome. In other words, trying to help yourself hurts the group; if everybody tries to gain individually, they all end up worse off.
In such games, the "help-yourself-at-the-expense-of-the-group action" is often called the "defect" choice, while the "don't-grab-for-personal-gain-so-as-to-leave-the-group-better-off action" is often called the "cooperate" choice.
In this example, a fishing crew helps itself individually by catching as many fish as it can. This is the "defect" strategy. If all crews act in this way, however, the stock of fish can become so depleted that (eventually) there are fewer fish for any boat to catch. [This negative-for-everybody outcome may take some time to develop.]
There are strong individual incentives to choose "defect", and in this example it appears that just about all fishing crews have done so. Perhaps some sort of formal international agreement will allow them to restrain their fishing (to switch to the "cooperate-cooperate" outcome) in order to let the fish population build back up. [A formal agreement may be necessary because each fishing crew would see no gain from an individual decision to reduce its fish catch.]
Question 16 answer is: c. I and IV
Explanation: The definition of a "public good" has two elements. (i) When a new person starts to receive benefits from a public good, the amount of the good available for others isn't reduced (in other words, each unit of the good is available for anybody who wants to benefit from it). I.e., the good is "nonrival". (ii) It is impossible (or difficult and expensive) to prevent any person from benefiting from the good, even if that person didn't pay for it. I.e., the good is "nonexcludable".
From the quotes given in the question, quote I captures the nonexcludable aspect, and quote IV captures the nonrival aspect.
In contrast, quotes II and III would be relevant for a (pure) private good -- a person can't consume the good unless he or she pays for it, and if one person consumes a unit of a good, there is one less unit of it available for everybody else.
Question 17 answer is: d. releasing sterilized insects to prevent disease-carrying bugs from breeding
Explanation: The definition of a "public good" has two parts. First, the good must be "nonrival" -- having one more person benefit from the good doesn't reduce the amount of the good from which others can benefit. Second, the good must be "nonexcludable" -- a person who doesn't pay for a good can't (or can't at reasonable cost) be prevented from benefiting from it.
Answers (a), (b), and (c) all fail to have at least one of these characteristics. In fact, producing computers has neither -- the use of a computer can be restricted to those who pay for it; when one person uses a computer, there is one less computer for everybody else to use.
If a concert venue isn't crowded, it's possible that the experience could be nonrival -- an additional person might be able to enter the building without lessening the exprience of those already in it. Access to a concert, however, can be fairly easily restricted to those who bought a ticket; a concert is an excludable good.
Driving on a city street is -- in most locations (the central city of London excepted) -- something anybody can do; such driving is therefore nonexcludable. If the streets are crowded, however, having one more car on those roads does reduce the benefits experienced by others (since as additional vehicle adds to congestion and slows travel time). In this situation, therefore, driving is a rival activity.
In contrast, a program to reduce the number of disease-carrying bugs helps all the people who reside in an area. Having one more person in the area does not lessen the benefits felt by others. Furthermore, the reduction of infectious bugs can't be limited to only certain people in an area. Of these four choices, therefore, the reduction of insect populations is the best example of a nonrival and nonexcludable good.
While the question did ask this, it's worth noting the implication of this conclusion. Of these four alternatives, the one that is mostly unlikely to be provided in an efficient amount by the private market -- and therefore the one that most likely requires government involvement -- is insect control.
Question 18 answer is: b. 1
Explanation: Remember that the definition of a "public good" implies the following. If one unit of a public good is available to the members of a community, then each member of the community can fully "consume" (and fully benefit from) that unit. [While it doesn't really matter in this question, this is true regardless of whether or not a person pays for the good.] For example, if one unit of a public good is provided to a two-person community, then each person in the community benefits from one whole unit of the good (so that the unit is not "divided up," in which case each person would benefit from only one-half unit).
If one unit of the good is provided, both People A and B can fully benefit from it. In fact, Person A gets a benefit valued at $14 from one unit of the good, and Person B gets a benefit valued at $8. In this case, making one unit of the good available to the group produces $22 worth of benefit for the community. Since a unit of the good costs only $20 to purchase, there is a positive net benefit (the benefit exceeds the cost). In other words, it is effcient to provide the first unit.
For the second unit, the benefits are $12 and $6. If that second unit was provided, it would be fully available to both people, and the community as a whole would receive $18 from it. Since a unit of the good costs $20, the summed benefits of the unit are less than the unit's cost, and providing the unit would create a negative net benefit (it would not be efficient).
The same conclusion holds for the third unit, which would provide only $14 of benefit to the community.
Note the providing a unit can be efficient even if no single person gets a benefit from it that exceeds its cost. Since we are analyzing a public good that is available to all, we must sum the benefits that all the members of the community receive, and compare that sum to the cost of the item.
Note also that this question asks only about whether or not purchasing the good would create a positive or negative net benefit. It does not ask whether or not the good actually will be purchased. Due in part to the incentive of a person to free ride that exists for a public good, the outcome of whether or not a public good will be purchased depends (in part) on how the purchase would be financed.
Suppose, for instance, that this good would be purchased only if one person decided to pay for it voluntarily. Furthermore, suppose that each person considered only his or her own private benefits and costs when deciding whether to buy it. With these assumptions, no purchase would occur, because a single person (who gets at most a benefit of $14) would never find it worthwhile to pay $20 to buy the good. Thus, private, voluntary, decision-making may fail to acquire a good even when it would be socially-efficient to do so.
Question 19 answer is: d. both private good X and public good Y ; only private good X
Explanation: When considering a (pure) private good, we know that one unit of the good can be consumed by only one person, and that those who don't pay for the good can be prevented from consuming it. Here, a good that is valued at $3 per unit costs only $2 per unit to produce. Clearly, value exceeds cost, so there would be a net gain to society if (many units of) this good were produced. Furthermore, the information in the question implies that potential consumers of private good X would be willing to pay more for the good than what it costs to produce it (it is only by paying their own money for the good that they can get access to it). The production of this good thus appears to be a potentially profitable business opportunity. We can therefore be confident that a free-market economic system would produce private good X.
The characteristics of a (pure) public good are: (i) when one person consumes some of the good, the amount available for others is not reduced, and (ii) those who don't pay for the good can not be prevented from consuming whatever units of it are produced. it. Here, one unit of the good costs $600 to produce, and would create $900 worth of value (since that one unit would provide $3 of value to all 300 people). There would thus be a net gain to society if (at least) one unit of this good was produced.
We can't, however, be sure that public good Y will actually be produced. This is because the characteristics of a public good create an incentive for an individual to "free ride" by not paying for such a good himself, while hoping to be able to benefit from whatever quantities of the good are purchased (using the payments made by others). In this case, each of the 300 people might know that it would be good thing if public good Y were somehow paid for, but each person also knows that his or her best personal outcome would be if he or she paid nothing, but others paid enough for Y to be funded. Since everybody feels this incentive, a world in which all payments are voluntary may well see few people who are willing to contribute their own money to help buy public good Y. It's possible that some kind of organized effort could raise enough money to pay for Y, but we certainly can't be confident of that outcome.