Microeconomics Questions
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EC489.03 – Boğaziçi UniversitySummer 2011 by Arhan ErtanStudy Questions1.For each of the following production functions, draw a diagram showing thegeneral shape of its corresponding isoquant. Comment on the ease at which labor and capital can be substituted for one another relative to the other two production functions.a. Q = K + L.b. Q = K0.5L0.5.c. Q = min(K, L).Answer:a. Isoquants are straight lines from the horizontal axis to the vertical axis. Perfect substitutability.b. Isoquants are curves with slope -1 in the middle and asymptotically approaching both the vertical and horizontal axes. Limited substitutability.c. Isoquants are L-shaped. No substitutability.2. A firm uses 3 factors to produce its output. Its production function is f(x, y, z) =min{x3/y, y2, (z4 - x4)/y2}. If the amount of each input is multiplied by 2, by which factor will its output be multiplied?Answer: 4.3.Which of the following production functions exhibit constant returns to scale?Explain. In each case y is output and K and L are inputs.(1) y = K1/2L2/3. (2) y = 3K1/2L1/2. (3) y = K1/2 + L1/2. (4) y = 2K + 3L.Answer: 2 and 44. A competitive firm has a production function described as follows. “Weeklyoutput is the square root of the minimum of the number of units of capital and the number of units of labor employed per week.” Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely.a. Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (Be careful at the boundaries.)b. If the wage is w = $1 and the price of output is p = $4, how much labor will the firm demand in the short run?c. What if w = $1 and p = $10?d. Write down an equation for the firm’s short-run demand for labor as a function of w and p.Answer:a. MP = 1/(2L1/2) if L < 16, MP = 0 if L > 16.b. 4.c. 16.d. L = (p/2w)2.5. A firm has the production function Q = X1/21X2. In the short run it must use exactly15 units of factor 2. The price of factor 1 is $75 per unit and the price of factor 2 is$2 per unit. Write down the firm’s short-run marginal cost functionAnswer:MC(Q) = 10Q/156.Mr. X’s total costs are 2s2 + 40s + 40. If he repairs 10 cars, what will be hisaverage variable costs?Answer: $607.Miss Z’s production function for comic books is 0.1J1/2L3/4, where J is the numberof jokes and L is the number of hours of cartoonists labor that he uses. If she can vary both jokes and cartoonists’ labor and if old jokes cost $2 each andcartoonists’ labor costs $18 per hour, then the cheapest way to produce comics books requires using jokes and labor in which ratio of J/L?Answer: 68.The snow removal business in East Icicle, Minnesota, is a competitive industry.All snowplow operators have the cost function C = Q2 + 4, where Q is the number of driveways cleared. Demand for snow removal in the town is given by Q d = 120 - P. What is the long-run equilibrium number of firms in this industry? Answer: In LR, P = minAC = 4 (Q i = 2). Then Qtotal = 120 – 4 = 116 and n=589.Merih produces plastic dog dishes using a process that requires only labor andplastic as inputs and has constant returns to scale. With the process she iscurrently using, a laborer can turn out 30 dog dishes an hour. The wage rate is $9 per hour. The plastic in a dog dish costs Merih $0.10. She has no other costsbesides labor and plastic. Merih faces a perfectly competitive market for plastic dog dishes, and she decides that she is maximizing profits when she makes 300 dog dishes an hour. What is the market price of dog dishes?Answer: $0.4010.A competitive firm has a single factory with the cost function c(y) = 4y2 + 89 andproduces 28 units in order to maximize profits. Although the price of output does not change, the firm decides to build a second factory with the cost function c(y) = 8y2 + 39. To maximize its profits, how many units should it produce in the second factory?Answer: Equate MCs in both factories: Y1=28, Y2=1411.A competitive firm has a long-run total cost function c(y) = 5y2 + 1.125 for y > 0and c(0) = 0. Write down its long-run supply function.Answer:y = p/10 if p > 150, y = 0 if p < 15012.The bicycle industry is made up of 100 firms with the long-run cost curve c(y) = 2+ (y2/2) and 60 firms with the long-run cost curve c(y) = y2/10. No new firms can enter the industry. What is the LR industry supply curve at prices greater than $2? Answer:y = 400p13.On a tropical island there are 100 potential boat builders, numbered 1 through100. Each can build up to 20 boats a year, but anyone who goes into the boat-building business has to pay a fixed cost of $19. Marginal costs differ from person to person. Where y denotes the number of boats built per year, boat builder 1 has a total cost function c(y) = 19 + y. Boat builder 2 has a total cost function c(y)= 19 + 2y, and more generally, for each i, from 1 to 100, boat builder i has a costfunction c(y) = 19 + iy. If the price of boats is 25, how many boats will be built per year?Answer: 24 boat builders, each will produce 20 (to minimize AC) = 480 boats14.In the absence of government interference, there is a constant marginal cost of $4per ounce for growing marijuana and delivering it to buyers. Suppose thatgovernment authorities seize shipments whenever they find them and resell the marijuana that they seize on the open market. The probability that any shipment of marijuana is seized is 0.50. If a shipment is seized, there is no other punishment besides loss of the marijuana that is seized. What is the effect of the government action on the equilibrium price of marijuana?Answer: It raises the equilibrium price by $4.15.In a certain industry, the supply curve of any firm is S i(p) = p/2. If a firm produces5 units of output, what are its total variable costs?Answer: $25.16.The demand for a monopolist’s output is 7,000 divided by the square of the pricein dollars that it charges per unit. The firm has constant marginal costs equal to 1 dollar per unit. At what level of output is his total revenue maximized and at what level of output is his profit maximized?Answer: It should charge a price of 2 dollars to maximize profits.17.A profit-maximizing monopolist faces a downward-sloping demand curve that hasa constant elasticity of -3. The firm finds it optimal to charge a price of $12 for itsoutput. What is its marginal cost at this level of output?Answer: $8.18.A monopolist produces at a point where the price elasticity of demand is -0.7 andthe marginal cost is $2. If you were hired to advise this monopolist on how toincrease his profits, would you recommend to increase or to decrease its output? Answer: Decrease its output.19.A major software developer has estimated the demand for its new personal financesoftware package to be Q = 1,000,000P-2 while the total cost of the package is C = 100,000 + 25Q. If this firm wishes to maximize profit, what percentage markup should it place on this product?Answer: 100%.20.A monopolist sells in two markets. The demand curve for her product is given byp1 = 122 - 2x1 in the first market and p2 = 306 - 5x2 in the second market, where x i is the quantity sold in market i and p i is the price charged in market i. She has a constant marginal cost of production, c = 6, and no fixed costs. She can charge different prices in the two markets. What is the profit-maximizing combination of quantities for this monopolist?Answer: Make MR = 6 in both markets. Then: x1 = 29 and x2 = 3021.A careful analysis of demand for bubble-gums reveals a strange segmentation inthe market. It is produced by the process Q = min{R/3, W}, where R and W are the only inputs needed to produce bubble-gums and P R = $1, P W = $5. If demand for bubble-gums by senior citizens is described by Q0 = 500P-3/2 while demand by those under 65 years old is Q y= 50P-5, how should bubble-gums to be priced to maximize profits?Answer: Optimal production: Use 3R and 1W. So, MC = 3 + 5 = 8. Make MR = 8 in both markets: Therefore price = $24 for senior citizens and = $10 for those younger22.Suppose that the demand curve for mineral water is given by p = 40 - 12q, wherep is the price per bottle paid by consumers and q is the number of bottlespurchased by consumers. Mineral water is supplied to consumers by amonopolistic distributor who buys from a monopolistic producer, who is able to produce mineral water at zero cost. The producer charges the distributor a price ofc per bottle. Given his marginal cost of c per unit, the distributor chooses anoutput to maximize his own profits. Knowing that this is what the distributor will do, the producer sets his price c so as to maximize his revenue. The price paid by consumers under this arrangement isAnswer: $30.23.Rabelaisian Restaurants has a monopoly in the town of Upper Glutton. Itsproduction function is Q = 40L, where L is the amount of labor it uses and Q is the number of meals produced. In order to hire L units of labor, RabelaisianRestaurants must pay a wage of 40 + .1L per unit of labor. The demand curve for meals at Rabelaisian Restaurants is given by P = 5.25 - Q/1,000. The profit-maximizing output for Rabelaisian Restaurants isAnswer: 2,000 meals.24.An industry has two firms each of which produces output at a constant unit cost of$10 per unit. The demand function for the industry is q = 1,000,000/p. TheCournot equilibrium price for this industry isAnswer: $20.25.An industry has two firms producing at a constant unit cost of $10 per unit. Theinverse demand curve for the industry is p = 110 - .5q. Suppose that firm 1 is a Stackelberg leader in choosing its quantity (i.e., firm 1 chooses it’s quantity first, knowing that firm 2 will observe firm 1’s quantity when it chooses its ownoutput.) How much output will firm 2, the follower, produce?.Answer: 50 units.26.The demand for y is given by y = 256/p2. Only two firms produce y. They haveidentical costs c(y) = y2. If they agree to collude and maximize their joint profits, how much output will each firm produce?Answer: 227.A game has two players. Each player has two possible strategies. One strategy isCooperate, the other is Defect. Each player writes on a piece of paper either a C for cooperate or a D for defect. If both players write C, they each get a payoff of $100. If both players write D, they each get a payoff of 0. If one player writes C and the other player writes D, the cooperating player gets a payoff of S and the defecting player gets a payoff of T. To defect will be a dominant strategy for both players ifAnswer:S < 0 and T > 100。