帮写Econ 702: Homework 2代写数据结构语言

Econ 702: Homework 2

March 5, 2024

Abstract

This homework covers the material on investment and an extension to the RBC Model.

1 Short Response Questions

Each of the following questions are worth 10 points.

1. Consider the following coupon bond: Suppose the bond pays a coupon payment of 100 for the next 3 years, and then makes a final payment of 1000 in the fourth year. The interest rate is 10%. Write the formula for how you would price this bond (use the values of the payment listed above):

2. True or False: As interest rates rise, bond prices rise.

2 Longer Response Questions

The first of the free-reponse questions is worth 20 points. The second free-response question is worth 60 points.

1. Investment with uncertainty. The world lasts two periods. The XYZ company is a large internet-based retailer. At t = 2, it will pay a dividend of $150 per share if the economy is doing well and $50 per share if the economy is doing poorly. Consider a household that will consume $40,000 if the economy is doing well and $30,000 if the economy is doing poorly. Its preferences are given by u(c) = 1−σ/c1−σ. The interest rate is 10%. Suppose the probability the economy is doing well is 75%.

(a) Derive an expression for the price at which the household would be indifferent with respect to buying a share in the XYZ company. Hint: the household already knows how much it is going to consume in period 2 and suppose that the household’s decisions are consistent with its Euler equation.

(b) Use the formula you found in part (a) to determine the price if σ = 2.

2. RBC Model with Labor. Consider a 2-Period version of the RBC model from class, but now assume that labor is an input into production. In this formulation of the model, households have 1 unit of time per-period and they can either enjoy leisure or work for a wage wt (for t = 1, 2). In this formulation of the model, the households recieve labor income from firms and recieve firm profits (just like in class). Assume households preferences are given by U(C, 1 − L), and that agents discount the second period at rate β. Assume that the production function is AtKt αL 1−αt. Assume that the capital level in the first period is given (i.e., we know K1), and assume that there is full depreciation of capital.

(a) Define a competitive equilibrium for this economy.

(b) Solve the firm’s problem and obtain closed from expressions for the real interest rate r1 and the wage rates w1 and w2.

(c) Solve the households maximization problem, the firm’s maximization problem and the resource con-straints to come up with a system of equations that pin down the competitive equilibrium. Hint: you should have 5-equations and 5-unkowns. The unknowns will be (C1, C2, L1, L2, K2).

(d) Define the social planner’s problem in this economy. Explicity write out the maximization problem that the planner solves.

(e) Derive a system of equations that pin down the solution to the planners problem. Hint: you should have 5-equations and 5-unkowns. The unknowns will be (C1, C2, L1, L2, K2).

(f) How do the solutions to the competitive equilibrium and social planners problem relate to one another?

What is the intuition for this result?