Economics Final Exam

In the lecture, we have been assuming that firms can charge any price they want in a Bertrand game, for instance, $1.2745. In reality, firms usually only specify the dollar and the cent of a good. For instance, a firm may only be able to charge $1.27 or $1.28 instead of $1.2745 for a good. Under this more realistic assumption, consider a two-firm Bertrand competition with homogeneous goods where Firm 1 has a constant marginal cost of $2 and Firm 2 has a constant marginal cost of $3. When the two firms charge the identical price, each firm attracts half of the consumers. The market demand function is Q(p)=10-p. Which of the following is a Bertrand equilibrium? (In the following vectors, the first dimension refers to the price charged by firm 1, and the second dimension refers to that of firm 2.)

($2.99, $3) ($2.99, $2.99) and ($2, $2) cannot be Bertrand equilibrium, because Firm 2 has half of and market share but suffers from a loss, which is worse than charging $3 and earning zero. In the other three options, Firm 2 charges $3, so you first need to identify the best response of Firm 1: Firm 1 will slightly undercut the price of Firm 2 and acquires the entire market, so $2.99 is Firm 1's best response when Firm 2 charges $3. Given Firm 1 charges $2.99, Firm 2's best response is to stay out of the market, and charging $3 is a best response.

In a two-player game, consider two strategy profiles (A, X) and (B, Y). According to the definition of Pareto domination, we say the profile of strategies (A, X) Pareto dominates (B, Y) if and only if _______.

(A, X) is at least as good as (B, Y) for both players and (A, X) is better than (B, Y) for at least one player By definition of Pareto domination, the profile of strategies (A, X) Pareto dominates (B, Y), if (A, X) is at least as good as (B, Y) for both players, and (A, X) is better than (B, Y) for at least one player.

Suppose there are two firms producing crude oil in the market. The market demand curve is linear and is given as follows: Q(p) = 30 - p, where Q is the number of barrels of crude oil. The marginal cost to produce per barrel of crude oil is $3. If the two firms compete in a Stackelberg model, what will be the equilibrium output produced by each firm be?

(q1=13.5, q2=6.75) Writing p in terms of q in the demand function, we have the inverse demand function p(q)=30-q, where q=q1+q2 is the total output level. Hence, firm 2's revenue is (30-q1-q2)q2. The marginal revenue of firm 2 is 30-q1-2q2. By setting MR2=MC2, we have 30-q1-2q2=3. This means that the optimal strategy of firm 2 is q2(q1)=13.5-0.5q1. Notice that firm 2 can observe the action taken by firm 1. Firm 1 cannot observe the action taken by firm 2, but Firm 1 can anticipate firm 2 using strategy q2(q1)=13.5-0.5q1. Hence, when firm 1 chooses q1, the market price is p=30-q1-(13.5-0.5q1)= 16.5-0.5q1. Hence, the revenue of firm 1 is (16.5-0. 5q1)q1 and marginal revenue of firm 1 is 16.5-q1. By setting MR1=MC1, we have q1=13.5. q2(13.5)=13.5-0.5*13.5=6.75.

Consider a sequential-move version of a rock-paper-scissor game. Players sequentially form one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper; a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. Suppose Player 1 moves first and Player 2 moves afterwards. In this game, what is the subgame perfect Nash equilibrium payoff of Player 1?

-1

Consider a sequential-move version of an integer game between two players: Marilyn and Noah. Each of the player is required to announce a positive integer. In other words, a player can announce 1, 2, 3, 4, ... Marilyn announces the number first and Noah announce the number afterwards. Notice that this game is different from the games we learned in class in that each player has infinitely many actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both 0. In this game, what is the subgame perfect Nash equilibrium payoff of Noah?

1

Jim left his previous job as a sales manager and started his own sales consulting business. He previously earned $70,000 per year, but he now pays himself $25,000 per year while he is building the new business. What is the economic cost/opportunity of the time he contributes to the new business?

$45,000 per year The economic cost is the opportunity cost. By earning a salary and manages his own firm, Jim gives up the opportunity to earn additional $70000-$25000.

A monopolist

1. produces less than the competitive outcome. 2. sells at a price higher than the competitive price. 3. sells at a price higher than its marginal cost at q*.

Consider the utility function U(x,y)=x+3y. The marginal rate of substitution of good x for good y is given by:

1/3

Bob views apples (a) and oranges (o) as perfect substitutes in his consumption. When we put apples on the horizontal axis and oranges on the vertical axis, MRSao = 0.5 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget is $30 per week. Given Bob's budget constraint, what is his utility maximizing choice?

10 pounds of oranges and no apples

A monopoly faces a market demand Q(p)= 2000-4p and has total cost C(q)=200q. Suppose that the government intervenes the market and splits the monopoly into two firms with costs C1(q)=200q and C2(q)=200q. If the newly created firms compete in prices (Bertrand competition), then the total output level after this intervention is?

1200 In symmetric Bertrand equilibrium, every firm charges a price that is identical to marginal cost of production. So the market price is 200. The total output level is thus 2000-4*200=1200.

Evan has preference that is represented by the utility function U(x,y)=x1/2y1/2. The MRSxy is equal to y/x. This preference is smooth and the utility maximization problem has interior solution. If Evan has income I=$2000 and Px=$50 and Py=$25, what is Evan 's consumption of good x?

20 units

A monopoly faces a market demand Q(p)= 2000-4p and has total cost C(q)=200q. Suppose that the government intervenes the market and splits the monopoly into two firms with costs C1(q)=200q and C2(q)=200q. If the newly created firms compete in prices (Bertrand competition), then equilibrium market price after this intervention is?

200 In symmetric Bertrand equilibrium, every firm charges a price that is identical to marginal cost of production. So the market price is 200.

John consumes apples and bananas. John 's utility function is U(x, y)=x+y where x is the number of apples and y is the number of bananas. He has 40 apples and 5 bananas. Which of the following bundles would John prefer to his?

25 apples, 25 bananas

A monopoly faces a market demand Q(p)= 2000-4p and has total cost C(q)=200q. Suppose that the government intervenes the market and splits the monopoly into two firms with costs C1(q)=200q and C2(q)=200q. If the newly created firms compete in Cournot model, then equilibrium profit earned by each firm after this intervention is?

40000 Writing p in terms of q in the demand function, we have the inverse demand function p(q)=500-0.25q, where q=q1+q2 is the total output level. Hence, firm 1's revenue is (500-0.25q1-0.25q2)q1. The marginal revenue of firm 1 is 500-0.5q1-0.25q2. By setting MR1=MC1, we have 500-0.5q1-0.25q2=200. This means that the reaction curve for firm 1 is q1(q2)=600-0.5q2. Similarly, you can find firm 2's reaction curve: q2(q1)=600-0.5q1. Solve the system of equations, we have q1=q2=400. So the total output level is 800. The market price is p(800)=500-0.25*800=300. So the equilibrium profit earned by each firm is (300-200)*400=40000

The price elasticity of demand for gasoline is estimated by some researchers to be -0.02. Approximately, what percentage change in the price of gasoline induces an increase of 1% in its consumption?

50% Decrease -0.02=(1% change in consumption)/(percentage change in price). Hence, percentage change in price =1%/(-0.02)= -50%.

Sue views hot dogs and hot dog buns as perfect complements in her consumption, and the corners of her indifference curves follow the 45-degree line. Suppose the price of hot dogs is $5 per package (8 hot dogs), the price of buns is $3 per package (8 hot dog buns), and Sue's budget is $48 per month. What is her optimal choice under this scenario?

6 packages of hot dogs and 6 packages of buns Sue's indifference curves are right angles. The corner fall on the 45 degree line. By observing the indifference map, you should find that Sue's utility maximization market basket is always along the 45-degree line. This means that Sue will always choose to buy the same number of packages of hot dogs and buns. When buying 1 packet of hot dog and 1 packet of buns, the cost is $8. By spending all $48, Sue will buy 48/8=6 packages of hot dogs and 6 packages of buns.

A monopoly faces a market demand Q(p)= 2000-4p and has total cost C(q)=200q. Suppose that the government intervenes the market and splits the monopoly into two firms with costs C1(q)=200q and C2(q)=200q. If the newly created firms compete in quantities (Cournot competition), then equilibrium total output level of the two firms after this intervention is?

800 Writing p in terms of q in the demand function, we have the inverse demand function p(q)=500-0.25q, where q=q1+q2 is the total output level. Hence, firm 1's revenue is (500-0.25q1-0.25q2)q1. The marginal revenue of firm 1 is 500-0.5q1-0.25q2. By setting MR1=MC1, we have 500-0.5q1-0.25q2=200. This means that the reaction curve for firm 1 is q1(q2)=600-0.5q2. Similarly, you can find firm 2's reaction curve: q2(q1)=600-0.5q1. Solve the system of equations, we have q1=q2=400. So the total output level is 800.

Suppose there are two firms producing crude oil in the market. The market demand curve is linear and is given as follows: Q(p) = 30 - p, where Q is the number of barrels of crude oil. The marginal cost to produce per barrel of crude oil is $3. If the two firms compete in a Stackelberg model, what will be the price of crude oil be in the Stackelberg equilibrium?

9.75 Writing p in terms of q in the demand function, we have the inverse demand function p(q)=30-q, where q=q1+q2 is the total output level. Hence, firm 2's revenue is (30-q1-q2)q2. The marginal revenue of firm 2 is 30-q1-2q2. By setting MR2=MC2, we have 30-q1-2q2=3. This means that the optimal strategy of firm 2 is q2(q1)=13.5-0.5q1. Notice that firm 2 can observe the action taken by firm 1. Firm 1 cannot observe the action taken by firm 2, but Firm 1 can anticipate firm 2 using strategy q2(q1)=13.5-0.5q1. Hence, when firm 1 chooses q1, the market price is p=30-q1-(13.5-0.5q1)= 16.5-0.5q1. Hence, the revenue of firm 1 is (16.5-0. 5q1)q1 and marginal revenue of firm 1 is 16.5-q1. By setting MR1=MC1, we have q1=13.5. q2(13.5)=13.5-0.5*13.5=6.75. The total output level is 13.5+6.75=20.25. Hence, the market price is p(20.25)=30-20.25=9.75.

A monopolist faces a demand Q(p)=2000-4p and has total cost C(q)=200q. What is the monopolist's maximal profit?

90000

Suppose two firms have equal constant marginal cost and no fixed cost. The market demand function is linear. Bertrand equilibrium results in ____ total output level and a ____ price than Cournot equilibrium.

A higher; a lower

Suppose capital is fixed and labor is the only variable input. When the output level is q=10, we know that MC(10)=4 and AVC(10)=7. It must be true that ____.

Average variable cost decreases at q=10. When marginal product is lower than average product, AP is decreasing.

Consider the following three market baskets: Basket A: 6 units of food and 3 units of clothing, Basket B: 8 units of food and 5 units of clothing, Basket C: 5 units of food and 8 units of clothing. If preferences satisfy all four basic assumptions, which of the following statement is correct?

B is preferred to A. The assumption of more is better tells us that B is preferred to A. No other conclusions can be made without additional information.

Suppose the demand function of Good X is QX=I/(PX+PY) and that of Good Y is QY=I/(PX+PY). The two goods, X and Y, are:

Complements

Jose works for the economic research department of the local utility company in his city. He is interested in the effect of a price increase in the demand for their services. He calculates that the price elasticity for the demand is -2.3. This means:

Demand will fall approximately by 2.3% if price increases by 1%. Price elasticity measures the relative change in consumption in proportion to the relative change in price. Thus, demand will fall approximately by 2.3% if price increases by 1%.

Collusion on a high price can earn higher prices and higher profits under the Bertrand model, but why is this an unlikely outcome in practice?

Each collusive firm has an incentive to gain market share at the expense of the other firms by cutting prices. In the language of game theory, collusion Pareto dominates the Bertrand equilibrium for firms. But collusion is not a Nash equilibirum: each firm has the incentive to lower the price to increase market share.

Consider the utility function U(x, y)=4x+2y. An agent who has this utility function prefers which of the following baskets:

Evaluate the utility of each option and the one with greatest utility will be the preferred basket.

The equilibrium in Nash equilibrium must be Pareto efficient.

False

When the assumption "more is better" is imposed on consumer behaviors, the income effect can never be negative.

False

Decreasing returns to scale" and "diminishing returns to a factor of production" are two phrases that mean the same thing.

False To determine returns to scale, all inputs have to change. However, diminishing return to a factor of product only describes the change in one input

Suppose an accountant offers personalized prices for different customers for the essentially the same tax preparation service. The price is based on each customer's income level, family situation, asset level, etc, so that the price is close to the customer's willingness to pay. This can be viewed as a practice of ______.

First-degree price discrimination

Natalia and her sister, Gina, have the following utility functions on the number of slices of pizza (x) and cans of soda (y) they consume in the semester. Natalia's is U(x, y)=3x+2y and Gina's is V(x, y)=4x+2y. If we plot their indifference curves with x measured in the horizontal axis and y measured in the vertical axis, we find that:

Gina's indifference curves are steeper than Natalia's. Both sisters have linear indifference curves. Take for instance the point (1,1). The equation of Natalia's indifferent curve through (1,1) is 5=3x+2y, and the equation of Gina's indifference curve through (1,1) is 6=4x+2y. Thus for Natalia y=5/2-3x/2 and for Gina y=3-2x. Thus, Gina's indifference curves are steeper: the slope is more negative. The only point in Gina's indifference curve through (0,0) is (0,0). The utility of Natalia in her indifference curve through (3,2) is 13. Thus, (0,0) is not on Natalia's indifference curve through (0,0).

Which of the following statement is NOT true?

If Good X and Good Y are perfect complements and the kinks of your indifference curves follow the 45-degree line. You should follow the rule that MRS equals the price ratio to find the optimal market basket.

What is different between the Cournot and Stackelberg models?

In Cournot model, firms make output decisions simultaneously; in Stackelberg model, firms make output decisions sequentially. Both models are quantity competition model, not price competition ones. Cournot model is a simultaneous move game. Stackelberg model is a sequential-move game

Suppose the demand function of Good X is QX=0.5I/PX and that of Good Y is QY=0.5I/PY. The two goods, X and Y, are:

Independent

Which of the following is true concerning the substitution effect of a decrease in price?

It always will lead to an increase in consumption. When price decreases, substitution effect always leads to an increase in consumption of the good.

Which of the following is true regarding utility along a price-consumption curve?

It changes from point to point.

Linda receives a raise at work and her income increases. How does her budget line change?

It makes a parallel shift outward. When income increases, the budget line shifts outward parallelly.

Jane's Engel curve for the consumption of food shows:

Jane's consumption of food as a function of income, all the other constant Engel curve shows the relationship between the consumption of food and income.

Suppose isoquant curves are smooth and bend in towards the origin and the cost minimization point is determined by the tangent of the isocost lines and the isoquant. Except ____, all the other options characterize the cost minimization input bundle. (If a condition characterizes the cost minimization input bundle, the condition holds only at the cost minimization input bundle.)

MRTS = MPL /MPK MRTS = MPL /MPK is the analytical definition of MRTS. It holds no matter the firm is minimizing cost or not. All the other expressions are cost minimizing condition.

At the profit-maximizing level of output q>0, which of the statement is wrong

Marginal profit is maximized

The assumption that preferences are complete:

Means that the consumer can compare any two market baskets of goods and determine that either one is preferred to the other or that she is indifferent between them

In the simultaneous-move rock-paper-scissors game, is there a Nash equilibrium? (We do not consider randomization.)

No

Rock paper scissors is a two-player game, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper; a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. In this game, is (paper, paper) a Nash equilibrium?

No

The following problem is designed to check that you understand the definition of Nash equilibrium. Consider an integer game between two players: Marilyn and Noah. Each of the player is required to announce a positive integer. In other words, a player can announce 1, 2, 3, 4, 5..., but cannot announce "infinity". Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has infinitely many actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both 0. Does this game have a Nash equilibrium?

No This game does not have any Nash equilibrium. Suppose there is a Nash equilibrium in which Marilyn announces M and Noah announces N. Consider the following two cases. (1) If M<N or M=N, then Marilyn is not playing her best response: she can be better-off by announcing N+1. Hence, (M,N) is not a Nash equilibrium. (2) If M>N, then Noah is not playing his best response: he can be better-off by announcing M+1. Hence, (M,N) is not a Nash equilibrium. In summary, there is no Nash equilibrium.

Which of the following statement is correct?

No matter a consumer maximizes utility or not, MRSXY=MUX/MUY.

Andy uses his entire budget to purchase 2 units of Good X and 3 units of Good Y. The price of Good X is $1 and that of Good Y is $2. His marginal utility from Good X is 2 and that of Good Y is 6. Is his current consumption decision optimal?

No, he should increase Good Y consumption and reduce Good X consumption.

Alfred derives utility from consuming iced tea and lemonade. For the bundle he currently consumes, the marginal utility he receives from iced tea is 16, and the marginal utility he receives from lemonade is 8. Instead of consuming this bundle, Alfred should:

None of the other options is necessarily correct. When he maximizes his utility and the solution is interior, it must be true that: MRSXY =PX/PY. Without knowing price ratio, we do not know whether he has maximized his utility or not.

Ronny's Pizza House operates in the perfectly competitive local pizza market. If the price of cheese increases, what is the expected impact on Ronny's profit-maximizing output decision?

Output decreases because the marginal cost curve shifts upward

In a Cournot duopoly, we find that Firm 1's reaction curve to Firm 2's output is Q1 (Q2)= 100 - 0.75Q2, and Firm 2's reaction curve to Firm's 1 is output is Q2 (Q1)= 75 - 0.5Q1. What is the Cournot equilibrium outcome in this market?

Q1 = 70 and Q2 = 40

A competitive coffee shop has the following cost function C(q) = 200+0.1q2. What is the supply function of this shop?

S(p)=5p

At a coffee shop, the per oz price of a tall coffee (12 oz) is usually higher than that of a grande coffee (16 oz). We can say the coffee shop is practicing ____.

Second-degree price discrimination

In a local grocery store, avocado is priced "$1 each, 3 for $2". This can be viewed as a practice of ______.

Second-degree price discrimination

If an increase in the price of one good leads to an increase in the quantity demanded of another, the two goods are:

Substitutes

Suppose your utility function for food (F) and clothing (C) is u(F, C) = F + 4C. If you reduce your clothing consumption by 2 units, how much do you have to increase your food consumption in order to maintain the same utility level?

Suppose we put food on the horizontal axis and C on the vertical axis. We can find any indifference curve, for example, the one passing (F, C)=(1, 1) and compute its equation: F+4C=5. Then C=-0.25F+1.25k. MRSFC=0.25=|DC/DF|=|-2/DF |. Hence, |DF |=8

By which assumption, an indifference curve should never be upward sloping?

The assumption of more is better If the indifference curve is thick, then on the same difference curve, we can find (at least) two market baskets: a northeast one and a southwest one. The northeast market basket and the southwest one should be indifferent to each other. But this violates the more the better assumption.

By which assumption, an indifference curve should be thin lines rather than thick lines?

The assumption of more is better. If the indifference curve is thick, then on the same difference curve, we can find (at least) two market baskets: a northeast one and a southwest one. The northeast market basket and the southwest one should be indifferent to each other. But this violates the more the better assumption

Collusion can earn higher prices and higher profits under the Bertrand model, but why is this an unlikely outcome in practice?

The collusive firms have an incentive to gain market share at the expense of the other firms by cutting prices. Colluding on a high price Pareto dominates Bertrand equilibrium. However, in a noncooperative game, each firm has the incentive to lower the price and acquire more market share

Suppose Andy has a utility function of U (x, y) = 2x + y and a wealth level of 12. The price of good X is 2 and the price of good Y is 1. Which of the following statement is optimal?

There are multiple optimal market baskets.

If prices and income in a two-good society double, what will happen to the budget line?

There will be no effects on the budget line As both prices and the income double, the budget line is not changed.

A tennis coach charges $15 per hour for tennis lessons for children and $30 per hour for tennis lessons for adults. This can be viewed as a practice of ______.

Third-degree price discrimination

Both Sally and Sam receive a 5% raise in a single year. Sally increases her demand for ground beef, whereas Sam decreases his demand for ground beef.

This is possible if ground beef is a normal good for Sally, and is an inferior good for Sam.

Suppose the price elasticity of demand of movie tickets is equal to -1 throughout the curve. How do total expenditures on movie tickets vary along the demand curve?

Total expenditures remain the same between points along the demand curve. When demand has constant elasticity of -1, a 1% increase in price leads to a 1% decrease in quantity demanded. Hence, the expenditure/revenue does not change.

Giffen good is always an inferior good, but inferior good may not be Giffen good.

True

The Engel curve bends backward implies that the good is a normal good at low income level and is an inferior good at a high income level.

True

Which of the following statements is WRONG?

Under the first-degree price discrimination, social welfare is minimized.

Consider a sequential-move version of a rock-paper-scissor game. Players sequentially form one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper; a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. Suppose Player 1 moves first and Player 2 moves afterwards. In this game, consider the following strategy profile: Player 1 plays rock; if observing Player 1 plays rock/paper/scissor, Player 2 plays paper/scissor/rock. Is this strategy profile a subgame perfect Nash equilibrium?

Yes

Consider a sequential-move version of an integer game between two players: Marilyn and Noah. Each of the player is required to announce a positive integer. In other words, a player can announce 1, 2, 3, 4, ..., but no one can announce "infinity". Marilyn announces a number first and Noah announce a number afterwards. Notice that this game is different from the games we learned in class in that each player has infinitely many actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both 0. In this game, is there any subgame perfect Nash equilibrium?

Yes

Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of the player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both 0. Does Marilyn have a dominant strategy?

Yes

Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of the player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both 0. Does this game have a Nash equilibrium?

Yes

In the lecture, we have been assuming that firms can charge any price they want, for instance, $1.2745. In reality, firms usually only specify the dollar and the cent of a good. For instance, a firm may only be able to charge $1.27 or $1.28 instead of $1.2745 for a good. Under this more realistic assumption, consider a two-firm Bertrand competition game where both firms have a constant marginal cost of $2. The market demand function is Q(p)=10-p. In this game, is ($2, $2) a Bertrand equilibrium? Is ($2.01, $2.01) a Bertrand equilibrium? (In these vectors, the first dimension refers to the price charged by firm 1, and the second dimension refers to that of firm 2.)

Yes. Yes. Both are Bertrand equilibria. In the first Bertrand equilibrium, no firm has an incentive to charge a higher price - because it will end up losing all customers and thus earn a zero profit; no firm has an incentive to charge a lower price - because the firm will suffer from a lost. In the second Bertrand equilibrium, each firm earns positive profit. No firm has an incentive to charge a higher price - because it will end up losing all customers and thus earn a zero profit; no firm has an incentive to charge a lower price - because the firm will earn zero profit, which cannot be a profitable deviation.

A firm's expansion path is:

a curve that shows the least-cost combination of inputs needed to produce each level of output for given input prices.

The short run is:

a time period in which at least one input is fixed

Consider a production function F(K,L)= ALaKb, where A, a and b are positive constants. Then, F has increasing returns to scale if:

a+b>1 decreasing return to scale if and only of a+b<1, constant return to scale if and only if a+b=1.

When marginal product of labor increases first and then decreases, the marginal product curve cuts average product from _____, at the _____ point of average product.

above, maximum

We do not consider randomization. The relationship between a Nash equilibrium and an equilibrium in dominant strategies is that:

an equilibrium in dominant strategies is a special case of a Nash equilibrium.

Assume that average product for six workers is fifteen. If the marginal product of the seventh worker is eighteen,

average product will rise between between six and seven workers. When marginal product is higher than average product, AP is increasing.

Suppose that initially the prices of x and y are the same. If the price of good x doubles and the price of good y triples, while income is held constant, the budget line (x is measured in the horizontal axis and y in the vertical axis):

becomes flatter.

A monopolist maximizes profits by

by setting MR(q)=MC(q) at a q for which p(q) is at least AVC(q)

The difference between what a consumer is willing to pay for a unit of a good and what must be paid when actually buying it is called:

consumer surplus.

Bette's Breakfast, a perfectly competitive eatery, sells its "Breakfast Special" (the only item on the menu) for $5.00. The average variable cost is $3.95 per meal; the average fixed cost is $1.25 per meal. Bette should:

continue producing in the short run, but plan to go out of business in the long run.

Suppose good x and y are perfect substitutes to Nicholas, then the indifference curves of Nicholas looks are _.

downward sloping straight lines

According to the definition of Nash equilibrium, a strategy profile (S1, S2) is a Nash equilibrium when:

each player is doing the best it can, given its opponents' strategy.

By definition, a Nash equilibrium occurs if and only if:

each player is doing the best it can, given its opponents' strategy. In a Nash equilibrium, each player plays the best response given opponents' strategy

When a firm charges each customer the maximum price that the customer is willing to pay, the firm:

engages in first-degree price discrimination.

Envision a graph with meat on the horizontal axis and vegetables on the vertical axis. Vivian loves vegetables more and Mike likes meat more. Vivian's indifference curves should be _ than those of Mikes.

flatter

Suppose the isoquants are right angles and the kinks are on the K=2L line. The expansion path will:

follow K=2L.

The Bertrand equilibrium ____.

has the same social welfare with competitive equilibrium

Bill currently uses his entire budget to purchase 5 cans of Pepsi and 3 hamburgers per week. The price of Pepsi is $1 per can, the price of a hamburger is $2, Bill's marginal utility from Pepsi is 4, and his marginal utility from hamburgers is 6. Bill could increase his utility by:

increasing Pepsi consumption and reducing hamburger consumption. Marginal utility per dollar for Pepsi is 4/1=4. Marginal utility per dollar for hamburger is 6/2=3. Since marginal utility per dollar for Pepsi is higher and Bill has already used his entire budget, he can only benefit from increasing consumption of Pepsi and decreasing that of hamburger.

Consider the production function F(K, L)=KL. Then, this production exhibits ___?

increasing return to scales

Rather than charging a single price to all customers, a firm charges a higher price to men and a lower price to women. This ______.

is a practice of price discrimination.

Assume that beer is a normal good. If the price of beer rises, then the substitution effect results in the person buying ________ of the good and the income effect results in the person buying ________ of the good.

less; less

In the sequential version of a game using the same players, the same strategies, and the same possible outcomes as the original game, the subgame perfect Nash equilibrium ________.

may be different than the Nash equilibrium in the original game.

Assume that rice is a Giffen good. If the price of rice falls, then the substitution effect results in the person buying _ of the good and the income effect results in the person buying __ of the good. Overall, the person will buy __ of the good.

more; less; less When the price of rise falls, substitution effect results in an increase in the consumption of rice. This is true no matter the good in normal or inferior or Giffen. As the price of rice falls, there is an increase in real purchasing power, and thus the real income increases. However, a Giffen good is an inferior good. Hence, the income effect results in the person buying less of the rice. Overall, the income effect dominates for the Good to be Giffen.

Suppose isoquant curves are smooth and bend in towards the origin. When an isocost line is just tangent to an isoquant, we know that:

output is being produced at minimum cost. This is the condition for cost minimization. There is only one output but two inputs.

The demand curve facing a perfectly competitive firm is

perfectly horizontal

The demand curve facing a perfectly competitive firm is ___________.

perfectly horizontal The demand curve facing a perfectly competitive firm is perfectly elastic, so flat. This is because each firm is too small to affect the market price and can only treat the price as given.

In a Nash equilibrium,

players may or may not have dominant strategies.

If a consumer prefers market basket A to C and C to B, then according to transitivity, the consumer should _.

prefers A to B

Suppose that an agent has utility function U(x, y)=x+2y. What information is necessary to calculate the agent's optimal consumption of Good X?

price of Good X, price of Good Y, and income

An individual demand curve can be derived from the ________ curve.

price-consumption We construct a demand curve from the price-consumption curve. We construct an Engel curve from the income-consumption curve.

In comparing the Cournot equilibrium with the competitive equilibrium,

profit is higher, and output level is lower in Cournot. Cournot equilibrium has lower output level and high price than competitive equilibrium.

Relative to the Cournot equilibrium, the Bertrand equilibrium with homogeneous products ____.

results in a larger output at a lower price Bertrand equilibrium has the same output and price as the competitive equilibrium. Hence, Bertrand equilibrium has a larger output and a lower price than Cournot equilibrium.

Suppose good x and y are perfect complements to Nicholas, then the indifference curves of Nicholas looks are _.

right angles

Suppose price elasticity of demand of artichoke is equal to -0.5. When the price of artichokes is increases slightly, the total expenditure by consumers on artichokes will ________ and the number of artichokes sold will ________.

rise; fall The demand is inelastic. Thus, as the price falls, the quantity demanded increases but at a smaller percentage. Thus, the expenditure increases.

A firm produces autos following the production function q =F(K,L)= 5KL, where q is the number of autos assembled in a day, K is the number of robots used on the assembly line (capital) and L is the number of workers hired per hour (labor). If we use K = 10 robots and L = 10 workers in order to produce q = 450 autos per shift, then we know that production is:

technically feasible and inefficient.

Indifference curves are convex to the origin (namely, bow in towards the origin) because of:

the assumption of a diminishing marginal rate of substitution.

Suppose the assumption of more is better is satisfied. If indifference curves cross, then:

the assumption of transitivity is violated. If indifference curves cross, then either the assumption of transitivity is violated or the assumption of more is better is violated.

For a monopoly, marginal revenue is less than price because:

the firm must lower price if it wishes to sell more output.

A dominant strategy produces ________.

the highest payoff for every possible strategy of the other players.

A change in consumption of a good resulting from an increase in purchasing power, with relative prices held constant, is referred to as:

the income effect.

When the price faced by a competitive firm was $5, the firm produced nothing in the short run. However, when the price rose to $10, the firm produced 100 tons of output. From this we can infer that:

the minimum value of the firm's average variable cost lies between $5 and $10.

Suppose the indifference curves are smooth and the utility maximization solution is interior. When a person consumes two goods (A and B), that person's utility is maximized when the budget is allocated such that:

the ratio of the marginal utility of A to the price of A equals the ratio of the marginal utility of B to the price of B.

When labor (L) is on the horizontal axis and capital (K) is on the vertical axis, which is NOT a correct definition/description of the marginal rate of technical substitution:

the ratio of the prices of the inputs.

In the Stackelberg model, there is an advantage:

to being the first competitor to commit to an output level. In Stackelberg model, there is a first mover advantage.

When the marginal product drops to zero (and never goes up again),

total product is maximized.

Consider an economy with good X and good Y. Good X is on the horizontal axis and good Y is on the vertical axis. Anne currently consumes 50 units of good X and 30 units of good Y, where her MRS of X for Y is equal to 2. If she decreases her consumption of Y by 1 and increases her consumption of X by 2, her utility level _. We can approximately view the indifference curves as straight lines around the market basket (50, 30).

will increase Since MRSXY=2, she is willing to give up 2 units of Y to increase X by 1. Alternatively, she is willing to give up 1 unit of Y to increases X by 0.5. Now she decreases her consumption of Y by 1 but increases her consumption of X by 2. This means that her utility should increase.

Jason has utility function U(x,y)=x2y. Then, the equation of Jason's indifference curve through (2,1) is:

y=4/(x2) The utility level at (2, 1) is equal to 4. Hence, the indifference curve has function x2y=4. By solving y, we have y=4/(x2).