Advanced seminar in Economics

Week 13 - Review

Part a

1. Is the following an equation for a demand curve? Explain why or why not.

Q = 10 + 1

P2

2. Is the following an equation for a supply curve? Explain why or why not.

ln Q = 12 + 1

3 ln P

3. Find out |ε| for the following at P = 2.

(a) P = 10 − 1 5 Q

(b) Q = 20 P2

(c) MR = −2

4. Suppose two linear demand curves D1 and D2 have the same vertical intercept and D1 is steeper than D2. At any given P , which demand is more elastic?

P

D1

D2

0 Q

P

5. What is the law of diminishing returns?

6. What do we mean by an isoquant? Why is it downward sloping? Why is it convex?

(a) Find the equation for an isoquant with Q = 48 for the production function Q = 24L 1 4 K

1 4 . Prove that it is

downward sloping and convex.

(b) What kind of returns to scale does the production function given above exhibit? What do we mean by that? What would the long-run average total cost look like?

(c) Suppose price of labor (w) = 1 and price of capital (r) = 2. The market price for the output produced is P = 12. For the production fumction given above,

i. find out the short-run cost function C (Q) |K=81, and ii. the profit maximizing choice of output and labor in the short-run. How much is the profit?

Part b

7. A price discriminating monopolist sells in two separate markets with demand curves given by: P1 = 80 − 2.5x and P2 = 92 − 2y, respectively. If her marginal cost is given by MC = 5Q, where Q = (x + y), what quantities should she sell and what prices should she charge in the two markets?

8. Suppose the only long-run adjustment is free entry or exit of firms. What is the difference between the short-run equilibrium conditions faced by a perfectly competitive firm and a monopolistically competitive firm? How about the long-run equilibrium conditions?

9. Amy and Soma discover a stream that flows wine. Amy and Soma decide to bottle the wine and sell it. The marginal cost and the fixed cost to bottle wine are $2 and 0 respectively. The market demand for bottled wine is given by: P = 602 − 2Q, where Q is the total quantity of bottled wine produced and P is the market price of bottled wine. Answer the following questions.

(a) What are the economically effi cient (in other words, perfectly competitive) price and quantity of bottled wine? How much will be the profit?

(b) Suppose that Amy and Soma act as Cournot duopolists. How much bottled wine will each one of them produce? At what price? How much profit will each one of them earn?

(c) Suppose Soma is a "naive" Cournot duopolist so that Amy can act as a Stackelberg leader. What level of output will each one of them produce? What will be the price of wine? How much will be the profit for each one of them?

(d) Ignoring antitrust considerations, would it be profitable for firm Amy to merge with Soma and share the profit equally? Explain.

10. There are only two food trucks in a town. Their menus are not identical, but not totally different either. The price for each entree in a truck is the same. The trucks pick their prices and sell according to their demand. The demand curve in lunch hour faced by truck 1 is given by: x = 5 −p1 + p2 and by truck 2 is given by: y = 10 −p2 + 2p1. The costs are C1(x) = x and C2(y) = 2y, where truck 1 serves x consumers and truck 2 serves y consumers.

(a) Determine the reaction function for each truck.

(b) How many consumers will each truck serve in equilibrium? At what price? How much will be the equilibrium profit for each truck?

Part c

11. Now consider an open economy with government. Suppose it is described by the following equations:

C = 100 + 0.85 (Y −T) − 1000r I = 200 − 2000r,G = 500,T = 100 + 0.2Y

EX = 35,IM = 50 + 0.08Y

L = 20Y − 600000r M = 2200000,P = 110,rrr = 0.2

(a) Find out the equation for the IS and LM curves (do not round up your answer, leave the fraction as it is).

(b) Find out the equilibrium r and Y.

(c) If G increases by 40, then by how much do the IS and LM curves shift and by how much does Y change? How much is the crowding out effect? If Fed monetizes the additional budget deficit to eliminate crowding out, do they need to buy bonds, or sell bonds? Worth how much?

(d) Suppose Ḡ = 500 again (so refer back to parts a and b of this question). Now if the Fed purchases securities worth of 33000 and there is no leakage of excess reserves, then by how much does it change the money supply? By how much do the IS and LM curves shift and by how much does Y change?

(e) Find out the equation for AD curve (referring to the set of equations given at the beginning of this question).