HYT ECONOMICS

Reading assignment: Sections 10-12, 28. 1. Consider an agent who values consumption in period O and 1 according to the following utility function: of is a discount factor (a $ 1) which indicates that the agnet prefers to consume today more than be can tomorrow. Suppose that the agent is given a total wealth today of w and that he may save any portion of this money in order to consume tomorrow. If he saves money he is paid interest r. This the agents budget constraint is: Itr - =0 (a) By renaming variables, notice that this problem is identical to the regular cobb douglas problemn. (b) Solve for the agents marshallian demand functions. (c) At what relation of & and r will the agent consume the same amount in each period? (d) Suppose that instead of being given a fixed endowment, the agent instead has access to a production technology that can make two products s, if that can be sold at prices p., p- The technology is limited by inputs so that at most: Pty=2 Solve for the optimal amount of r and y produced that maximize the agents profits. (e) Suppose that r is the amount of production that can be made in period 0 and y is the amount of production made in period 1. Suppose that pr =1, p, = 1,r= 0 Why can we seperate the production decision from the consumption decision in this problem? Give a value for s such that consumption is held constant in each period and the agent exactly consumes his production. 2. The legrangian multipliers in economies are often called "shadow costs". In this problem we will try to see where this term comes from and build intuition on how to use them to answer economic relevant questions. (a) Lets start with a very simple problems. W = max 2r- 12 I ST : ICK\fSolow-Swan Growth Model 1. Solow model as we have specified in our class: write down 5 endogenous variables, 5 equations, and exogenous variables/parameters of the Solow model. Show and explain how the system of five equations can be reduced into one equation in understanding economic growth in this model economy. (Hint: What is the equation we use to draw the Solow-diagram?) (10 points) 2. Based on the equation you got from the question 1, draw the Solow-diagram. Be sure you clearly label each axis. Be sure to clearly indicate which part of graph comes from which part of equation. (8 points)Homework 4 1. According to the Solow growth model, what would the impact of increased immigration be on total income (total output)? And on income per capita? Answer this question with the help of a graph. 2. Explain why 'technology' has low excludabilityConsider a variation to the baseline Solow growth model without population or technological progress. The per-capita production function is given by yt = f(kt) = kta, where 0