关键词 > Economic代写
Dynamic Economic Theory Problem Set 1 2022
发布时间：2022-09-14
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Dynamic Economic Theory
Problem Set 1
2022
For all questions, if necessary, make appropriate assumptions.
1. Consider the following two-period maximization problem where the consumer solves
u (c2 )
c1 ,c2 1 + ρ
s.t. a1 = (1 + T) (a0 + y1 - c1 )
a2 = (1 + T) (a1 + y2 - c2 )
a1 , a2 > 0
a0 is given.
Here, the condition at > 0 for both t = 1, 2 represents the borrowing limit in financial markets.
(a) Derive the inter-temporal budget constraint of the consumer.
(b) Graphically illustrate the budget constraint a household.
(c) Suppose the utility function of the consumer is u (ct ) = log ct and the resources are given as a0 = 5, y1 = 4, and y2 = 6. For simplicity, T = ρ = 0. Solve for the optimal consumption and savings choice.
(d) At the beginning of time 1, the interest rate T unexpectedly increases from T = 0 to TH . Explain its effects on c1 , a1 , and c2 .
2. Consider an economy consists of consumers who live for T periods. The preference is additive and separable:
T − 1
Consumers enter the labor market at age 0 and earn y0 , and their annual earnings increase at rate γ > 0 until t < N - 1. For t > N , consumers retire and exit the labor market. Consumers may borrow or save as long as aT > 0.
(a) Suppose the initial endowment is a0 = 0, and the interest rate and time preference are the same as zero: r = ρ = 0. Derive the inter-temporal budget constraint.
(b) Define the maximization problem of a consumer and find the optimal consumption as a function of y0 . What is the marginal propensity to consume out of labor income?
(c) What is the marginal propensity to consume out of labor income for age t = 0 to N - 1? Graph- ically illustrate the life-cycle pattern of MPC.
(d) Now suppose there is influx of newly born generation entering the economy in each period. The size of population of each generation is the same, and they lives for T periods and share the same endowment/ preference schedules. Would the consumption-income relation be consistent with Keynesian theory? Explain.
