Questions .

Please answer each question in detail

1) Consider the following technology: c(yi) = yi2 +2yi +4.

Many firms have access to this technology, in fact so many that there is not room for all to profitably operate in the industry. The market demand for the product is given by, P = 30-Y , where Y is the market quantity. Assume also that these firms are price takers, and entry / exit is costless.

A) What is the long-run free entry equilibrium per- firm quantity produced by each firrm in the industry? Explain (10 pts)

B)Do you have enough information to determine the number of firms who operate in such a long-run free entry equilibrium? If so, what is the number and justify your solution. If not, explain what other information you would need. (10 pts)

C) Is the price-taking behavioral assumption sensible for this industry? Explain (10 pts)

2) A monopolist has access to an industry with market demand D(p) = 24-2p and its cost function is c(y) = y2.

A)Determine its proft - maximizing output level y* and the market price p(y*). (5 pts)

B)Calculate the monopolist s profit. (5 pts)

C)Compute the point-elasticity of demand at the profit maximizing output level y* . Would the monopolist ever operate at a point elasticity |e(y)|

D)Suppose this monopolist is regulated to produce at that quantity where price equals average cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario. (5 pts)

E)Calculate the profit for the monopoly if it is regulated to produce where price equals average cost. Explain. (5 pts)

F)Suppose this monopolist is regulated to produce at that quantity where price equals marginal cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario. (5 pts)

G)Calculate the profit for the monopoly if it is regulated to produce where price equals marginal cost. (5 pts)

H)Is this is a natural monopoly? Explain. (5 pts)

3) A monopoly is facing two types of consumers. Type 1 consumer has relatively low demand given by pL(yL) = 8 yL and type 2 consumer has relatively high demand given by pH(yH) = 10 yH. The firm's marginal cost is MC = 0.

A)Suppose the two types are observable and the firm offers two packages using the two-part tarrifs pricing scheme (it charges a fee as well as a per unit price). What quantities and fees maximize the firms profit? Show these outcomes on graphs. (8 pts)

B)Now suppose that the firm is unable to distinguish the types, would the pricing scheme from part (a) work if the firm kept offer the same quantities yL and yH? (6 pts)

C)If the firm is unable to distinguish between the two types, but wants to offer the two different quantities you found in part (a), what fees should it charge to the different types of consumers? (8 pts)

D)Based on the pricing scheme used in part (c), calculate the consumer s surplus (for both types) and the producer s surplus. Do we have DWL in the market?

5. Gamma Distribution. Let U and V be continuous independent random variables and let W = U + V. Show that the probability density function of W can be written as fw(w) = fv(w- ufo(u) du = fu(w - v)fv(v) du where fo(u) and fv(v) are the density functions of U and V, respectively. Let X1, X2, ..., Xn ~ Exp(A) be a sequence of independent and identically distributed ran- dom variables, each following an exponential distribution with common parameter > > 0. Prove that if Y = IM then Y follows a gamma distribution, Y ~ Gamma (n, 1) with the following probability density function: (Av)"-1 fr(y) = de-4Y, y 20. (n - 1)! E Show also that E(Y) = and Var(Y) =Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements, state whether the statement is true, false, or uncertain, and give a complete and convincing explanation of your answer. Note: Such explanations typically appeal to specific macroeco- nomic models. 1. A tax on consumption is equivalent to a tax on labor income. 2 An increase in government spending without a commensurate increase in taxes will increase national income. 3. In the recent past, the Federal Reserve has dramatically increased the money supply, but output, employment and prices have all increased very slowly. Such an outcome is evidence in favor of the quantity theory. 4 An increase in government spending without a commensurate increase in taxes will increase welfare. 5. A permanent increase in productivity should cause permanent increases in both con- sumption and employment. 6 The lowering of a country's sovereign debt rating is equivalent to an increase in every. one's income tax rate and having the revenues thrown into the ocean.1. Question #26 in Chapter 13's Chapter Review, in the "Challenges" section-p. 266 of the textbook. This is a monopoly question, about a "natural monopoly." You may want to review what chapter 13 says about this type. The particular firm in this question, a cable company, like all natural monopolies, has a low, constant MC, and really big fixed costs, which mean that throughout the likely size range of the market it serves there's steadily declining ATC (or AC in the graph). This is quite realistic: a cable company would indeed have very low MC to supply service to a new customer, and very high fixed costs of building and maintaining the whole cable network. 2. Consider the payoff matrix below, which shows the decision airlines faced when the idea of having "loyalty programs" (known as frequent flyer programs, with perks for loyal customers). Here's a hypothetical payoff matrix for a situation where there are just two airlines; payoffs are in millions of dollars of profit per year. For simplicity, think of this as a "one-shot" game, i.e. played one time, once and for all. Delta Don't have a Have a Frequent Frequent Flyer Flyer loyalty United loyalty program program Don't have a Frequent Flyer 0, 0 -250, 250 loyalty program Have a Frequent Flyer loyalty 250, -250 -100, -100 program (a) Does United have a dominant strategy? Explain why or why not. (b) Does Delta have a dominant strategy? Explain why or why not. (c) What is the solution to the game, and is it a Nash equilibrium? Explain. (d) Review what the text says about the "Prisoners' Dilemma." Is this an example of a Prisoners' Dilemma?Consider the Solow model in discrete time. The following system of equations fully describe the economy: Y1: = C: + It Y1: : ArF[KrINr) : ArKgerma I, = 5r Kr+1 : (1 5)Kc + I: S, = 31',- Y defines income, (I defines consumption, I investment, 3 saving, K the capital stock, N employment {or labour) and A the state of technology; 6 E (0,1) is the rate of capital depreciation, s E [0.1) the saving rate and o E (0,1) is the capital elasticity of output. The previous equations describe a closed economy with no government. We further assume no technological progress, normalising for A, = 1, and no population growth. We assume that both the participation rate (labour force over population) and the unemployment rate are constant, which means that the labour force is constant; so, N, = N. (i) Express the above equations in per worker form, defined by lower- case letters, and derive the fundamental law of motion of the Solow model. What does this equation show? [10 marks] (ii) Explain how and why the economy starting from an initial quite low level of capital, Kn, will reach a steady state equilibrium. Compute capital per worker, output per worker, investment per worker, and consumption per worker in steady state equilibrium. What determines output per worker in the long run? Draw a graph with capital per worker at time t on the horizontal axis and output per worker at time t on the vertical axis to depict a steady-state equilibrium. Show also in the graph consumption per worker and investment per worker. [10 marks] (iii) Assume an economy that is in steady-state equilibrium and experiences an increase in the saving rate. Explain in words what will happen to this economy initially, but also in the long run, meaning the impact on both output per worker and its growth rate. Show this in a graph (similar to the previous one). Should we expect consumption per worker to rise in the long run? Explain your answer. [10 marks] (1") Consider two economies, economy X and economy I, which share exactly the same attributes {i.e., characteristics), apart from the saving rate; in particular, economy X has a higher saving rate. In the steady state, which economy is going to have the higher output per worker, the higher growth rate of output per worker, and higher welfare for their citizens? Consider now, that they also differ in their initial stock of capital; in particular, the economy 2 has a higher initial stock of capital. Does your answer now change, and why? Consider now, instead, that economy I invests more in education than economy X. Does your answer now change, and why? [10 marks] Consider the discussion between innovation and imitation in endogenous technological progress. Comment briefly on the statement that poorer countries can grow largely by imitating. How should governments design patent laws? [10 marks]