Microeconomics homework help me please/
10. Diamond Coconut Economy with uniform idiosyncratic preferences Time: Discrete, infinite horizon Geography: A trading island and a production island. Demography: A mass of 1 of ex ante identical individuals with infinite lives. Preferences: The common discount rate is r. Consumption of ones own produce yields 0 utils. Consumption of someone's good one likes yields u utils. The share of individuals whose goods I like is o. Whether an individual likes my good or not is independent of whether I like hers. (So she likes my good with probability of too.) Productive Technology: On the production island individuals come across a tree with a coconut with probability a each period. The cost of obtaining the coconut is c which is uniformly distributed over (0, 1). Assume that u 0. Households receive labor income and profits from firms. They pay taxes on their labor income, keeping the fraction S,, and receive government goods. Individual households, being atomistic, take G, as given. Households save by purchasing risk-free bonds. Let B, denote the quantity of bonds bought at time t, measured in terms of output. 1 unit of bonds delivers (1 + r,) units of output at time t + 1. Households face the usual initial, non-negativity and No-Ponzi-Game conditions. (a) Solve the consumer's and the producer's problems. (b) Note that there is no capital in this economy, so that bonds represent trades between consumers. Imposing equilibrium, find the resource constraint and the labor allocation condition. Use this result to express output and consumption in terms of the after-tax rate S,, and then solve for the equilibrium value of (1 + r,). (c) Do higher labor tax rates (lower values of S, ) increase or decrease output? Briefly explain in terms of income and substitution effects. 2 (d) Let lower-case letters with carats " " denote deviations of logged variables around their steady state values. Show that the log-linearized expressions for labor hours and output are: 03, 030.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.Q4. Pistaferri opens his 2003 paper on the intertemporal labor supply effects of wage changes with the following: "A long-standing question in labor economics is whether and to what extent individual labor supply responds to anticipated wage changes (also known as evolutionary wage changes). This effect is measured by the intertemporal elasticity of substitution..." a. Why is it important that wage changes used to identify the intertemporal labor supply elasticity use only anticipated changes in wages? Discuss the expected sign of the labor supply response to anticipated wage changes. If some of the wage changes are unanticipated, what will be the likely effect on the estimated labor supply response? Why? b. Pistaferri (2003) has data on individual's subjective expectations of their future wage growth, which he utilizes to decompose observed wages into three components: a. Anticipated, evolutionary movements in the wage over individuals' lifecycles b. Unanticipated permanent shifts in the future profile of wages c. Unanticipated transitory changes in wages Describe the expected effect of each of these components of wages on an individual's labor supply, drawing on standard models of utility maximization (leisure and consumption choice) over the lifecycle. C. Pistaferri's preferred estimate of the intertemporal labor supply elasticity for men (based on his measure of anticipated movements in the wage) is approximately 0.7. Compare this with the range of estimates of the intertemporal labor supply elasticities presented by MaCurdy (1981) or Altonji (1986). What might be responsible for differences in the estimates across these authors? What does it suggest about interpretation of the within-person relationship between labor supply and observed wages? Q5. Use this question to demonstrate your knowledge about empirical methods in Labor Economics. For each part, be as precise and comprehensive as possible. You are trying to measure the causal impact of college education on labor market outcomes. As an initial specification, you estimate with OLS, including a dummy variable for "College Graduate" as well as several control variables. Your focus is on the coefficient on College Graduate. You have data on many sets of siblings; where for each person you know their education level, labor market outcomes, who is related to whom, and each individual's covariates. A. Describe the "standard reasons" why we should be concerned about biased coefficients from estimating by OLS. B. What problems with OLS will propensity-score matching help to solve? What problems will it not help to solve? A colleague suggests adding "family fixed effects" to your specification. C. In what key ways does this change the nature of the identifying variation? D. What types of biases do family fixed effects help to remove? E. What are some ways that this strategy could still lead to biased results? F. Are there reasons why this strategy could increase the bias? Describe why or why not. G. What are the reasons why this strategy might not lead to biased estimates, but still give different results than OLS estimates? For this last part of the question, put aside issues of biased coefficients. You are concerned about statistical inference, and consider bootstrapping. H Describe as carefully as possible how you would implement this. What exact steps would you take? (Note: do not describe the Stata command(s) you would use. Instead, describe the conceptual steps involved.) I. If you decide to not bootstrap, what would you do to get correct statistical inference?Question 2 (50 points) This question considers the macroeconomic effects of a collapse in consumer demand in the New Keynesian model. There are a continuum of identical households. The representative household makes consumption (C) and labor supply (N) decisions to maximize lifetime expected utility: (1) subject to their budget constraint: Cit B, = IN, + (1 + i-1) P, (2) where w, is the real wage, N, is hours worked, B, are real bond holdings at the end of period t, i-1 is the nominal interest rate paid between t - 1 and t, A is the price of the final consumption good and D, are real profits from firms that are distributed lump sum. As usual, 0 0 and o > 0. Z, is a household preference shock, which is a way of generating shocks to demand. The production side of the model is the standard New Keynesian environment. Monopolistically competitive intermediate goods firms produce an intermediate good using labor. Intermediate goods firms face a probability that they cannot adjust their price each period (the Calvo pricing mechanism). Intermediate goods are aggregated into a final (homogeneous) consumption good by final goods firms. The production side of the economy, when aggregated and linearized, can be described by the following set of linearized equilibrium conditions (the production function, the optimal hiring condition for labor and the dynamic evolution of prices): (3) (4 ) * = BE(i+1) + Anice (5) The resource constraint is: 1 = a (6) Monetary policy follows a simple Taylor Rule: 1, =0.#, (7) The (linearized) preference shock follows an AR(1) process: (8) er is i.i.d. In percentage deviations from steady state: me, is real marginal cost, e, is consumption, w, is the real wage, fu is hours worked, y, is output. In deviations from 3 steady state: i, is the nominal interest rate, #, is inflation. A is a function of model parameters, including the degree of price stickiness." Assume that or > 1, 0
