ECO 521 University of Miami Macroeconomic Theory Problem Set Questions

User Generated

302831364_

Economics

ECO 521

University of Miami

ECO

Description

Please Complete the Problem Set.

Step-by-step solutions are required.

Tips for quality works.

Unformatted Attachment Preview

521/601 Adv. Macroeconomic Theory Problem Set 1 Professor: Miguel A. Iraola Fall 2020 Due Date: 9/23/2020 1. Finite Horizon: Consider the following Planner’s Problem: max {ct ,kt+1 }t=T t=0 : t=T X β t log (ct ) t=0 ct + kt+1 = Aktα , t = 0, 1, 2... s.t. ct , kt+1 ≥ 0, t = 0, 1, 2... k0 > 0, given. a) Suppose that A = 10, α = 0.3, β = 0.95, k0 = 0.05 y T = 1. Compute the optimal capital level at t = 1. b) (Voluntary) Provide a MATLAB program to compute the optimal sequence of capital for a generic finite horizon T. Plot the optimal sequence of capital and the steady state level of capital for T = 5, T = 10, T = 50 y T = 100. Guess the optimal sequence of capital for T = +∞. 2. Analitic Solution: Consider the following Planner’s Problem: max {ct ,kt+1 }t=∞ t=0 s.t. : t=∞ X β t [γlog (ct ) + (1 − γ)log(1 − nt )] t=0 ct + kt+1 = Aktα nt1−α , t = 0, 1, 2... ct , kt+1 ≥ 0, nt ∈ [0, 1] t = 0, 1, 2... k0 > 0, given. The notation is as follows: β ∈ (0, 1) is the subjective discount factor, γ ∈ (0, 1) determines the relative weight of each good in the utility function, ct denotes per capita consumption at t, kt is the stock of physical capital per capita at t, nt is the time per capita devoted to work at t, α ∈ (0, 1) is the capital income share and A > 0 is the Total Factor Productivity. Assume that the population size is normalized to one. 1 a) Provide the equations that characterize the solution. b) Write the optimal sequence of capital kt as a function of k0 . (Hint: You may assume that the time devoted to work is constant through time and that consumption is a constant fraction of output and then verify these assumptions). c) Compute the steady state level of capital kss > 0. Is it stable? 3. Solow Problem: Consider an economy such that the per capita production level is yt = ktα , with α = 0.4 where kt denotes the level of capital per capita. Assume that investment is a constant fraction of production s = 0.1. Assume that the depreciation of capital is δ = 0.08. Compute the steady state of this economy. Is it stable? 4. Changing Population: Consider the following optimization problem: max {Ct ,Kt+1 }t=∞ t=0 s.t. : t=∞ X β t log (Ct /Nt ) t=0 Ct + Kt+1 − (1 − δ)Kt = AKtα Nt1−α , t = 0, 1, 2... Ct , Kt+1 ≥ 0, t = 0, 1, 2... K0 > 0, given. Nt = η t N0 . The notation is as follows: Ct consumption at t, Kt stock of capital, Nt population size, δ ∈ (0, 1) depreciation rate, A > 0 total factor productivity η > 0 population growth rate. Note that the endowment of time each period is equal to one, and hence, the amount of time devoted to work is equal to the population size Nt . a) We are here assuming that individuals allocate all their endowment of time to work. Why? b) Define a balanced growth path and provide the equations characterizing it. 2
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached.

Que...


Anonymous
Great study resource, helped me a lot.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Similar Content

Related Tags