Micro theory Midterm 1.

If there is a price increase for a good that Susan consumes, her compensating variation is the change in her income that allows her to purchase her new optimal bundle at the original prices.

False

Nancy`s psychology teacher will give her a course grade that is the maximum of her scores on three midterm examinations. Nancy has convex preferences over the possible combinations of midterm scores.

False

The area under the marginal cost curve measures total fixed costs

False

The average variable cost curve must always be U-shaped

False

The economist's distinction between the long run and the short run captures the idea that quantities of some factor inputs can be varied in the short run but not in the long run.

False

The market for a good is in equilibrium when the government unexpectedly imposes a quantity tax of $2 per unit. In the short run, the price will rise by $2 per unit so that firms can regain their lost revenue and continue to produce.

False

With quasilinear preferences, the slope of the indifference curve is constant along all rays through the origin.

False

Fiery Demon is a rotgut whiskey made in Kentucky. Smoothy is an unblended malt whisky imported form Scotland. Ed regards these brands as perfect substitutes. When he goes into a bar, he sometimes buys only Fiery Demon. Other times he buys only Smoothy. This shows that Ed has unstable preferences.

False.

If the demand curve is a linear function of price, the the price elasticity of demand is the same for all prices.

False.

A monopolist with constant marginal costs faces a demand curve with a constant elasticity of demand lower than -1, and does not practice price discrimination. If the government imposes a tax of $1 per unit of goods sold by the monopolist, the monopolist will increase his price by more than $1 per unit.

True

Angela`s utility function is U (x1 + x2) = (x1 + x2)^3. Her indifference curves are downward sloping, parallel straight lines.

True

Charlie`s utility function is U (x,y) = xy^2. His marginal rate of substitution between x and y does not change if the amount of both goods doubles.

True

For a monopolist who faces a downward-sloping demand curve, marginal revenue is less than price whenever quantity sold is positive.

True

If preferences are homothetic and all prices double while income remains constant, then demand for all goods is halved.

True

If preferences are quasilinear, then for very high incomes the income offer curve is a straight parallel to one of the axes.

True

If the production function is f(x, y) = min{12x, 3y}, then there is convexity in production.

True

If there are constant returns to scale in a competitive industry, then the long-run industry supply curve for that industry is horizontal.

True

If there is one input used in production and if there are decreasing returns to scale, then the marginal product for the input will be diminishing.

True

In a monopolistically competitive industry with zero profit, each firm will produce less than the amount that minimizes average cost.

True

In the long-run, if there are increasing returns to scale, then average costs are a decreasing function of output.

True

It is possible to have an industry in which all firms make zero economic profits in long-run equilibrium.

True

Mr. O. Carr has the cost function 𝑐(𝑦) = 2y + 64 if his output, y, is positive and c(0) = 0. If the price of output is 12, Mr. Carr's profit maximizing output is zero

True

The utility function U( x1, x2) = 2lnx1 + 3lnx2 represents a Cobb-Douglas preferences.

True

Third degree price discrimination occurs when a monopolist sells output to different people at different prices, but every unit that an individual buys costs the same amount.

True

A firm faces competitive markets both for its inputs and its outputs. If its long-run supply curve is q =3p, then it cannot have constant returns to scale.

True

A competitive, cost-minimizing firm has the production function 𝑓 (𝑥, 𝑦) = 𝑥 + 2𝑦 and uses positive amounts of both inputs. If the price of x doubles and the price of y triples, then the cost of production will more than double

False

A discriminating monopolist is able to charge different prices in two different markets. If when the same price is changed in both markets, the quantity demanded in market 1 is always greater than the quantity demanded in market 2, then in order to maximize profits, the monopolist should charge a higher price in market 1 than market 2.

False

A firm produces one output with one input and has decreasing returns to scale. The price that it pays per unit of input and the price it gets per unit of output are independent of the amount that this firm buys or sells. If the government taxes its net profits at some percentage rate and subsidizes its inputs at the same percentage rate, the firm's profit-maximizing output will not change

False

A monopolist who is able to practice third degree price discrimination will make greater profits than a monopolist who is able to practice first degree price discrimination.

False

Consumer`s surplus is another name for excess demand.

False

If a competitive firm uses two inputs and has the production function 𝐹(𝑥, 𝑦) = 𝑥^1/2 + 𝑦^1/2 then its marginal cost curve is horizontal.

False

If melody has more classical records than rock and roll records she is willing to exchange exactly 1 classical record for 2 rock and roll records, but if she has more rock and roll records than classical records then she is willing to exchange exactly 1 rock and roll record for 2 classical records. Melody has convex preferences.

False

If preferences are homothetic, then the slope of the Engel curve for any good will decrease as income increases.

False

If the demand function is q = 3m/p, where m is income and p is price, then the absolute value of the price elasticity of demand decreases as price increases.

False

If the elasticity of demand curve for buckwheat is -1.25 at all prices higher than the current price, we would expect that when bad weather reduces the size of the buckwheat crop, total revenue of buckwheat producers will fall.

False

If the interest rate is 10%, a monopolist will choose a markup of price over marginal cost of at least 10%.

False

If the value of the marginal product of factor x increases as the quantity of x increases, and the value of the marginal product of x is equal to the wage rate, then the profit-maximizing amount of x is being used.

False

If there is a Cobb-Douglas utility, compensating and equivalent variation are the same.

False

A firm uses a single variable input x to produce outputs according to the production function 𝑓 (𝑥) = 300𝑥 + 6𝑥^2. This firm has fixed costs of $400. This firm's short-run marginal cost curve lies below its short run average variable cost curve for all positive values of x.

True

A competitive firm has a continuous marginal cost curve. It finds that as output increases, its marginal cost curve first rises, then falls, then rises again. If it wants to maximize profits, the firm should never produce at a positive output where price equals marginal cost and marginal cost decreases as output increases.

True

It is possible that a profit maximizing monopolist who is able to practice first degree price discrimination would sell a quantity x such that the demand curve for his product is inelastic when the quantity sold is x.

True.

A competitive firm's production function is 𝑓(𝑥, 𝑦) = 8𝑥^ 1/2 + 8 𝑦^1/2. The price of factor x is $1 and the price of factor y is $3. The price of output is $6. What is the profit-maximizing quantity of output? a. 256 b. 512 c. 252 d. 516 e. 244

a

In problem 2, Ambrose has indifference curves with the equation x2 = constant - 4x^1/2, where the larger constants correspond to higher indifference curves. If good 1 is drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Ambrose`s indifference curve when his consumption bundle is (16,10)? a. -0.50 b. -16/10 c. -10/16 d. -14 e. -4

a

Ambrose's brother Sebastian has a utility function 𝑈(𝑥1, 𝑥2) = 28𝑥^1/2+ 𝑥2, where 𝑥1 is his consumption of nuts and 𝑥2 is his consumption of berries. His income is $128, the price of nuts is $2, and the price of berries is $1. How many units of berries will Sebastian demand? a. 30 b. 60 c. 55 d. 49 e. There is not enough information to determine the answer.

a.

At a large institution of higher learning, the demand for football tickets at each game is 𝑡(𝑝) = 100,000 − 8,000𝑝. If the capacity of the stadium at that university is 60,000 seats, what is the revenue-maximizing price for this university to charge per ticket? a. $6.25 b. $5 c. $12.50 d. $3.13 e. $18.75

a.

Ms. Laura Mussel's preferences between golf and tennis are represented by 𝑈(𝑔,𝑡) = 𝑔𝑡, where g is the number of rounds of golf and t is the number of tennis matches she plays per week. She has $24 per week to spend on these sports. A round of golf and a tennis match each cost $4. She used to maximize her utility subject to this budget. She decided to limit the time she spends on these sports to 16 hours a week. A round of golf takes 4 hours. A tennis match takes 2 hours. As a result of this additional constraint on her choice... a. she plays 1 less round of golf and 1 more tennis match each week. b. she plays more golf and less tennis, but can't say how much. c. her choices and her utility are unchanged. d. she plays 2 less rounds of golf and 3 more rounds of tennis per week. e. There is too little information to tell about her choices.

a.

A monopolist receives a subsidy from the government for every unit of output that is consumed. He has constant marginal costs and the subsidy that he gets per unit of output is greater than his marginal cost of production. But to get the subsidy on a unit of output, somebody has to consume it. a. He will pay consumers to consume his product. b. If he sells at a positive price, demand must be inelastic at that price. c. He will sell at a price where demand is elastic. d. He will give the good away. e. None of the above.

b.

As assistant vice president in charge of production for a computer firm, you are asked to calculate the cost of producing 170 computers. The production function is 𝑞 = 𝑚𝑖𝑛{𝑥, 𝑦} where x and y are the amounts of two factors used. The price of x is $18 and the price of y is $10. What is your answer? a. $2,580 b. $4,760 c. $8,460 d. $6,180 e. None of the above.

b.

If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2 is always preferred to more, then indifference curves: a. slope downward. b. slope upward. c. may cross. d. could take the form of ellipses. e. None of the above.

b

Imagine first a drug dealer working in a competitive market with a constant marginal cost for producing marijuana of $6/oz. Suppose now that government authorities decided to seize the marijuana production whenever they find it. The production of marijuana is seized with a probability of 50%. If the production is seized, there is no other punishment besides loss of the marijuana. What happens to the new equilibrium prices with the new government's policy? (Hint: assume that the drug dealer is happy making zero economic profit.) a. prices remain unchanged. b. the equilibrium price increases by $6. c. the equilibrium price falls by $3. d. the equilibrium price increases by $12. e. the equilibrium price increases by $3

b.

Isabella's utility function is 𝑈(𝑥, 𝑦) = 4 𝑚𝑖𝑛{𝑥, 𝑦} + 𝑦. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, these indifference curves are: a. L-shaped with kinks where x = y. b. Made up of two line segments that meet where x = y. One of these line segments is horizontal and the other has slope −4. c. L-shaped with kinks where x = 5y. d. Made up of two line segments that meet where x = 5y. One of these line segments is vertical and the other has slope −1. e. V-shaped with kinks where x = 4y.

b.

A profit-maximizing competitive firm uses just one input, x. Its production function is 𝑞 = 4𝑥^1/2. The price of output is $28 and the factor price is $7. The amount of the factor that the firm demands is: a. 8. b. 16. c. 64. d. 60. e. None of the above.

c

Ambrose has indifference curves represented by the equation 𝑥2 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 − 4𝑥^1/2, where larger constants correspond to higher indifference curves. If good 1 is drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Ambrose's indifference curve when his consumption bundle is (9, 19)? a. −9/19 b. −19/9 c. −0.67 d. −22 e. −3

c

Katie Kwasi's utility function is 𝑈(𝑥1, 𝑥2) = 2(ln 𝑥1) + 𝑥2. Given her current income and the current relative prices, she consumes 10 units of x1 and 15 units of x2. If her income doubles, while prices stay constant, how many units of x1 will she consume after the change in income? a. 20 b. 18 c. 10 d. 5 e. There is not enough information to determine how many.

c

Mary Granola consumes tomatoes and nectarines. Mary's indifference curves are kinky. When she is consuming more tomatoes than nectarines, she is just willing to trade 3 tomatoes for 1 nectarine. When she is consuming more nectarines than tomatoes, she is just willing to trade 4 nectarines for 1 tomato. Let 𝑝1 be the price of nectarines, and 𝑝2 the price of tomatoes. Mary maximizes her utility subject to her budget constraint. Which statement is true? (Hint: Sketch one of her indifference curves.) a. When P1 > P2, she must consume only tomatoes. b. When P1 > P2, she must consume 3 times as many tomatoes as nectarines. c. When P1 > 3P2, she must consume only tomatoes. d. When 4P1 > P2, she must consume only nectarines. e. She must consume equal numbers of both.

c.

The production function of a competitive firm is described by the equation 𝑞 = 4𝑥^1/2(𝑦^1/2) The factor prices are 𝑝𝑥 = $1 and 𝑝𝑦 = $36 and the firm can hire as much of either factor it wants at these prices. The firm's marginal cost is a. decreasing. b. constant and equal to 19. c. constant and equal to 3. d. increasing. e. None of the above

c.

A firm has a production function 𝑓(𝑥, 𝑦) = 1.80(𝑥^0.80 + 𝑦^0.80)^3 whenever 𝑥 > 0 and 𝑦 >0. When the amounts of both inputs are positive, this firm has: a. increasing returns to scale if 𝑥 + 𝑦 > 1 and decreasing returns to scale otherwise. b. decreasing returns to scale. c. constant returns to scale. d. increasing returns to scale. e. increasing returns to scale if output is less than 1 and decreasing returns to scale if output is greater than 1.

d

A firm has fixed costs of $2,000. Its short-run production function is 𝑦 = 4𝑥^1/2, where x is the amount of variable factor it uses. The price of the variable factor is $1,600 per unit. Where y is the amount of output, the short-run total cost function is a. 5,000𝑦. b. 2,000 + 160𝑦. c. 2,000/𝑦 + 1,600. d. 2,000 + 100𝑦^2 e. 2,000𝑦 + 100.

d

An airline has exclusive landing rights at the local airport. The airline flies one flight per day to New York with a plane that has a seating capacity of 100. The cost of flying the plane per day is $4,000 + 10𝑞, where q is the number of passengers. The number of tickets to New York demanded is 𝑞 = 165 − 0.5𝑝. If the airline maximizes its monopoly profits, the difference between the marginal cost of flying an extra passenger and the amount the marginal passenger is willing to pay to fly to New York is a. $10. b. $100. c. $140. d. $160. e. None of the above.

d

If we graph Mary Granola's indifference curves with avocados on the horizontal axis and grapefruits on the vertical axis, then whenever she has more grapefruits than avocados, the slope of her indifference curve is −2. Whenever she has more avocados than grapefruits, the slope is −1/2. Mary would be indifferent between a bundle with 23 avocados and 29 grapefruits and another bundle with 31 avocados and: a. 25 grapefruits. b. 27 grapefruits. c. 19 grapefruits. d. 22 grapefruits. e. 23.50 grapefruits.

d

Suppose that the production function is 𝑓(𝑥, 𝑦) = (𝑥^a + 𝑦^𝑎)^𝑏, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution? a. For any value of a if b < 1 b. For any values of a and b if ab < 1 c. For any values of a and b if a > b d. For any value of b if a < 1 e. None of the above

d

The following relationship must hold between the average total cost (ATC) curve and the marginal cost curve (MC): a. If MC is rising, ATC must be rising. b. If MC is rising, ATC must be greater than MC. c. If MC is rising, ATC must be less than MC. d. If ATC is rising, MC must be greater than ATC. e. If ATC is rising, MC must be less than ATC.

d

A competitive firm uses two variable factors to produce its output, with a production function 𝑞 = 𝑚𝑖𝑛{𝑥, 𝑦}. The price of factor x is $8 and the price of factor y is $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x. In addition to the cost of inputs, the firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce 6 a positive amount? a. $44 b. $41 c. $29 d. $13 e. $21

e

Reginald is fond of cigars. His utility function is 𝑈(𝑥, 𝑐) = 𝑥 + 10𝑐 - 0.5𝑐^2, where 𝑐 is the number of cigars he smokes per week and 𝑥 is the money that he spends on the consumption of other goods. Reginald has $200 a week to spend. Cigars used to cost him $1 each, but their price went up to $2 each. This price increase was as bad for him as losing income of a. $5. b. $7.25. c. $9. d. $8. e. $8.50

e.

The inverse demand function for grapes is described by the equation 𝑝 = 676 − 9𝑞, where p is the price in dollars per crate and q is the number of crates of grapes demanded per week. When 𝑝 = 28 per crate, what is the price elasticity of demand for grapes? a. −9/676 b. −9/72 c. −72/28 d. −252/72 e. −28/648

e.

A decrease in income pivots the budget line around the bundle initially consumed

false

At a boundary optimum, a consumers indifference curve must be tangent to her budget line

false

If all prices are doubled and money income is left the same, the budget set does not change because relative prices do not change

false

If preferences are transitive more is always preferred to less.

false