Value: 60 points--30% of grade. All work must be shown or explained to earn credit.

1. Falls Ambulance Service has estimated a new production function for its ambulance deliveries per day:

Q = L^0.5K^0.6.

The price of labor and capital are $10 and $20 per unit. In the short-run, capital is fixed at 20 units.

1. Fill in the following. You may round values to the nearest whole number. (6)

L Q TFC TVC STC SAC AVC SMC(any method)

25 __ ___ ___ ___ ____ ____

49 __ ___ ___ ___ ____ ____ ____

100 __ ___ ___ ___ ____ ____ ____

b. Develop the equation relating STC to Q (i.e., find the short run total cost equation). (3)

c. Find the equation for SMC (2)

4. How much will the firm produce if the price of a delivery is $40? (2)

 

5. Explain the shape of Falls' long-run average cost (LAC) curve. Sketch the shapes of the LAC and LMC below. (4)

2. On the graph below, draw a consistent set of classical U-shaped set of short-run curves representing: AFC, SAC, SMC, and AVC. Label the axes and the curves. (5)

3. A firm in a perfectly competitive industry has the following short-run total cost:

STC = 200 + 40Q + 2Q²

a. If the price of the good is 100, how much will the firm produce? (3)

b. Determine the firm's profits. (2)

c. Determine the firm's AVC and its shut-down price. (3)

d. What is the firm's supply function? (3)

e. Assume that the total cost function given above also represents the long-run total costs. Determine the long-run equilibrium price for the industry. (3)

f. If the market demand is Qd = 10,000 - 20P, how many firms will there be in the industry in the long-run? (3)

4. A monopolist faces a demand: P = 1000 - 0.5Q and has a long-run marginal (and average) cost of 200.

a. Determine the profit-maximizing price and quantity. (4)

b. Determine the competitive price and output assuming that unit costs would remain at $200 in competitive markets. Also determine the welfare (efficiency) loss associated with the monopoly. Hint. A sketch may be helpful. (5)

5. A perfectly competitive market has the following demand and supply equations:

Qd = 1000 - 5P and Qs = -1000/3 + 10/3*P

a. Determine the equilibrium price and quantity. (4)

b. If P = 140, determine the excess demand or excess supply. (3)

c. Sketch the demand and supply curves from part (a) and show graphically how a $15 per unit tax on the seller affects quantity, the price paid by buyers, and the price received by sellers. (5)

 ANSWERS

1a. Q=30,42,60; TFC=400,400,400; TVC=250,490,1000; STC=650,890,1400; SAC=22,21,23; AVC=8,12,17; SMC=20,28 using finite changes or 24,34 using calculus

b. STC= P_LL + P_KK=10L+20K. However, Q=6L^0.5. Square both sides and solve for L=Q²/36.

Thus STC=10(Q²/36) + 400.

c.SMC=20Q/36= 0.56Q (Take the derivative of STC)

d.Set SMC=40 and solve. Q=72.

e.The production function shows increasing returns to scale. Thus LAC decreases and LMC lies below the LAC.

 2. SMC, AVC and SAC will be U-shaped. SMC will pass through the minimum points of the AVC and SAC. SAC must lie above the AVC and AFC (it is the vertical sum of the latter). AFC is a rectangular hyperbola.

3a. Set SMC=100 and solve. Q=15

b.TR=1500 and TC=1250; P =250

c.AVC=40+2Q i.e., linear with a vertical intercept of 40. P must be at least 40 to cover the minimum AVC.

d.Set P=SMC and solve: Q=10+0.25P for all P>40

e.Find the minimum of the LAC by setting its derivative =0. Thus Q=10 and LAC=80. Thus P=80 (to cover the minimum of the LAC).

f.At P=80, Qd=8400. Each firm produces 10 at P=80. Thus N=8400/10=840.

4a. Set MR=LMC. Thus Q=800 and P=600.

b.Pc=LMC=200. Thus Qc=1600. The welfare loss =0.5(Pm-Pc)Qc-Qm)=160,000.

5a. From Qd=Qs, P=160 and Q=200.

b. At P=140, Qd=300 and Qs=133. There is an excess demand or shortage of 167.

c. The supply curve shifts up by 15. It intersects the demand curve at a higher price (though less than 175) and a lower quantity than 200. The seller price after the tax is reduced below 160.