Question 1: Suppose you are given the following information about an industry:

Q_D = 8000 - 100p;

Q_S^SR = 20 + 700p;

c(q) = 20 + q²/20.

where q and c (q) stand for a firm's quantity supplied and cost function; Q_S^SR stands for the short-run industry supply curve. Q_D is the market demand curve, for both the short run and long run.

Assume that all firms are identical, and that the market is characterized by perfect competition, in both the long run and short run.

a. Solve for the (i) quantity supplied and (ii) profit of each firm in the short run.

b. Based on your answer in part (a), would you expect to see entry or exit in the industry during the transition from the short run to the long run? What effect will firm entry or exit have on market prices and firm profits during the transition? Explain.

c. What is the lowest price firms will sell their goods at in the long run? In other words, what is the long-run industry supply curve? Explain.

d. Suppose the government requires all firms to pay a fixed license fee to enter the market. Without any calculation, can you predict what will happen to the equilibrium price, number of firms, and firm profits in the long run?

Question 2: Susan uses her income (m) to consumes two goods (1 and 2). The prices are denoted by p₁ and p₂.Her utility function is U(x₁, x₂) = x₁^1/2 x₂.

a. State Susan's Marshallian demand functions for both goods in terms of income and prices.

b. Suppose that the market prices are p₁ = 1 and p₂ = 3, and Susan has a budget equal to m = 60. She also receives from the government a $30 coupon, which can be used to purchase good 1 (but not good 2).

i. Compute her optimal consumption bundle (x₁*, x₂*), and associated level of utility.

ii. Draw her budget line without coupon, the budget line with coupon, and two indifference curves to (roughly) show your answers for part b (i).

iii. In this context, would Susan be better off if the government simply gives her cash (which she can spend on both goods) rather than coupons? Explain briefly.

c. Use the Lagrangian approach to derive her Hicksian demand functions (in terms of p₁, p₂, and U) for good 1 and 2, respectively.

d. Compute the highest level of utility that she can achieve by using m = 60.

e. Solve for the total effect, income effect, and substitution effect of an increase in p_x, in terms of m and prices, using the Marshallian and/or Hicksian demand functions.

Question 3: Consider a manufacturing plant that produces clothes using labor and capital. Its technology is summarized by the production function: y = AK^1/2 + L^1/2, where y is the number of clothes produced; A represents the level of the so-called capital-biased technology; K stands for the amount of capital used, while L stands for labor used. The rental cost and wage rate (with the right normalization) are both equal to 1.

a. Solve for the short-run demand function for labor, L_SR (A, K, y). What is the marginal impact of an increase in A on K and LSR, respectively. Show your steps.

b. For y units of clothes, what are the

i. short-run total cost function (c);

ii. short-run marginal cost function (MC);

iii. short-run average variable cost function (AVC)

in terms of A, K, and y.

c. Derive the short-run supply curve (p(y)). Remember to specify the shut-down condition.

Let us now consider the long run, in which the firm can flexibly choose both capital and labor to minimize cost.

d. Derive the long-run cost function for the plant in terms of A and y, i.e., c(A, y). (Hint: replace both r and w by 1 before any derivation.)

e. Based on the cost curve, can you tell whether the technology exhibits increasing, decreasing, or constant returns to scale in the long run? Explain briefly.

f. How would a technological improvement affect the total cost of production for any level of output y?

g. How would a technological improvement affect the demand for capital relative to labor (i.e., K/L)? How can your answer shed light on the recent debate about how capital-biased technological advancement affects labor demand and potentially labor incomes?

Question 4: Consider the market for soft drinks, which can be described by the following equations:

Demand function: P = 10 - Q

Supply function: P = Q - 2

where P is the price per can of soft drinks and Q is the quantity.

a. Solve for the perfectly competitive equilibrium price and quantity (in the absence of government intervention)?

b. Suppose that the government imposes a tax of $2 per unit to reduce the consumption of soft drinks. Draw the graph of supply and demand curves, with P on the vertical axis, to illustrate the pre-tax and post-tax equilibrium. Remember to label the values of the old equilibrium, and the intercepts of ALL demand and supply curves drawn.

c. Solve for the new equilibrium quantity, the price buyers pay (per can of soft drinks), and the price sellers receive (per can)?

d. Compute the changes in consumer surplus, producer surplus, government revenue, and deadweight loss associated with the tax.

e. Despite the deadweight loss you computed in part d, provide and discuss one reason for why a government may want to tax the consumption of soft drinks. What does your answer tell you about the limitation of using a static frictionless equilibrium model to study welfare implications of policies?

Question 5 - Suppose Celgene Corporation, a biotech company, is a monopoly in the market for a cancer medication. The total cost of producing Q units of drugs is C(Q) = 2Q (i.e., there is no fixed cost of production).

The demand for drugs is Q = 30 - P

a. Find the level of output that maximizes Celgene's profits. What price would Celgene charge?

b. Suppose the government knows the demand and cost functions of the market. Find the price ceiling the government can impose to maximize social welfare (i.e. the sum of consumer surplus and producer surplus is maximized).

c. Provide one economic reason (not a political one) for why the US government would be very unlikely to impose such a price ceiling on Celgene in practice. Explain briefly.