11:56 PP - 1CO 0 & O all all 53% Edit 30 X STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics June, 2017 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 macroeconomic models. 1. As long as we have existence, the number of equilibria does not matter when it comes to comparative statics 2. Without immigration certain jobs in developed economies would not get done. 3. Raising tariffs on goods and services imported from the rest of the world will increase the average real wage of US workers. 4. The repeal of the Affordable Care Act will raise aggregate output in the long-term. 5. Output and inflation are positively correlated. 6. In dynamic general equilibrium macroeconomic models, the equilibrium gross interest rate (one plus the interest rate) tends to equal the inverse of the discount factor. Section 2. (Suggested Time: 2 Hours, 15 minutes) Answer any 3 of the following 4 questions. 7. Consider an economy composed of heterogeneous agents who can live for a maximum of two periods. Let s denote the survival rate from the first to the second period. Agents derive utility from consumption c according to utility function In(c) if alive, and derive zero utility if deceased. Agents discount utility of the second period with a discount factor of 8. In the first period, an agent receives an endowment w from a distribution with a probability density function f(w), and chooses consumption ci, savings &, and the amount of annuity a. The gross return on savings is (1 + 7). Each unit of annuities is sold at a uniform unit price of q, and gives one unit of goods in the second period if the agent survives to the second period, and zero units of goods otherwise. In the second period, living agents choose how much to consume, which is denoted by cz- Formally, the life-cycle problem for an agent who receives wage w is written as follows: DO DO W Tools Mobile View Share PDF to DOC O11:57 PP) - YCO 53% 8. Seigniorage in Sidrauski model with log-linear preferences Time: Discrete, infinite horizon Demography: A continuum, mass normalized to 1, of (representative) infinite lived con- sumer/worker households. There is a large number, mass N, of firms owned jointly and equally by the households. Preferences: The instantaneous household utility function over, consumption, cy, and real money balances, my, is y In(ct) + (1-y) In(m ) where y e (0, 1) and In(.) indicates the natural logarithm function. The discount factor is B e (0, 1). Technology: Aggregate output, Y = F(Kt, Ly ) where K, is the aggregate capital stock and Ly = 1 is the aggregate labor supply. The function F(.,.) is twice differentiable, strictly increasing in both arguments, concave and exhibits constant returns to scale. It will be helpful to use f (k) as the output per worker where k, is the capital stock per worker. Capital depreciates by a factor o in use each period. Endowments: Each household has one unit of labor and an initial endowment of capital ko. Each also has an initial nominal money holding Ho- Information: Complete, perfect foresight. Institutions: Competitive markets in each period for capital, the consumption good, labor and money. There is a government that has to meet the exogenous sequence of per capita expenditures, g. To do so, it issues new money and buys output from the market. Its policy instrument is the nominal money growth rate, o, such that H, = (1 +@) H-1. There are no cash transfers to households. The government injects money entirely by purchasing goods in the goods market for newly generated cash. (a) Using Mi+1 as period t nominal money demand, P, as the period t price of the consump- tion good, r, as the rental rate on capital and we as the wage paid per effective unit of labor, write down and solve the household's problem. (b) Solve the problem faced by the firms and, write down the market clearing conditions, the government budget constraint and the transversality condition. (c) Define a monetary equilibrium and solve for the equations that characterize the equilib rium. (d) Consider now of = g for all t. Write down the equations that characterize the steady state values k*, c', m* of the capital stock, consumption and real money balances as functions of the model parameters, f(.) and g. (e) By eliminating c* and m', solve for g as a function of the growth rate of the money supply, , the other model parameters and *. Note: &* is invariant to o, but (as g varies with o) c* is not. (f) Write down the problem faced by the government which wants to maximize government spending by controlling o. What is the value of o that maximizes government spending? What is the maximal amount of revenue that can be collected? 9. Consider the following version of a stochastic growth model. There are a fixed number of price-taking producers that solve max Il = Y - W.LP, Y = (LP )1-a, 00, 00. where xr > 0 follows a time invariant Markov process with the conditional probability density function (XX-1), and an initial value of Xo- Households receive labor income and profits from firms, and can store their assets K, and earn zero returns on the stored assets. As usual, assume that assets held at the beginning of period t + 1, Ki+1, are chosen in period t. Note that capital is used only as a storage device, and not as a factor of production. Households face the usual initial, non-negativity and No-Ponzi-Game conditions. (a) Define a competitive equilibrium b) Write down the firm's problem and find the first order conditions that maximize profits (c) Write down the household problem in a recursive form (Bellman's equation plus con- atrai its), and you need to replace the expectation operator with an integral to show how the expectation is made. Suppose we have internal solutions, find the first order conditions that maximize household utility.11:57 P P - YCD 53% 3 9. Consider the following version of a stochastic growth model. There are a fixed number of price-taking producers that solve max Il = Y - WIL!', Y = (LP)I-a, 00, 00. where x > 0 follows a time invariant Markov process with the conditional probability density function (XilX-1), and an initial value of Xo- Households receive labor income and profits from firms, and can store their assets K, and earn zero returns on the stored assets. As usual, assume that assets held at the beginning of period t + 1, Ki+1, are chosen in period t. Note that capital is used only as a storage device, and not as a factor of production. Households face the usual initial, non-negativity and No-Ponzi-Game conditions. (a) Define a competitive equilibrium b) Write down the firm's problem and find the first order conditions that maximize profits (c) Write down the household problem in a recursive form (Bellman's equation plus con- straints), and you need to replace the expectation operator with an integral to show how the expectation is made. Suppose we have internal solutions, find the first order conditions that maximize household utility. (d) Let lower-case letters with carats "" denote deviations of logged variables around their steady state values, and letters with subscriptss denote steady state values. In particular, we denote the unconditional expectation E(X,) = Xs, and define X, = log X, - log Xss- Linearize the equation that characterizes the labor-leisure trade-off. (e) Suppose the taste parameter for leisure can take two different values: X, E {n#, "1), with 7# > 71. Suppose the economy is at a steady state, and X, follows (x.|Xt-1) = 1/2 which is independent of X-1. What are the responses in the labor market after learning Xt = ny. Use the labor market equilibrium diagram to illustrate your finding. (f) Suppose the taste parameter for leisure can take two different values: X E {nm, "1}, with 7# > 72. Suppose the economy is at a steady state, and "(xX-1 )= [ 3/4 if Xt = X1-1 1/4 otherwise Would the labor market responses after learning X, = 7# differ from that derived in the previous part? Provide an intuitive explanation for your findings. (g) Is corr(Y, Y/L) a positive number, a negative number, or with the sign undermined? Provide an intuitive explanation for your findings. 10. One-sided search with tenure Time: Discrete, infinite horizon. Demography: Single worker who lives for ever. Preferences: The worker is risk-neutral (i.e. u(r) = r). He discounts the future at the rate T. Endowments: When unemployed the worker receives income b per period. Also with prob- ability a he gets an offer of employment at a wage w ~ F(.) on [0, w] where u > b. When employed the worker gets laid off (looses his job) with probability A. Also while em- ployed there is a probability y that the worker gets "tenure". When the worker has tenure he is no longer subject to layoff - he keeps his job for ever. (Getting tenure and getting laid off are mutually exclusive events and * ty