For this question the decision maker is the owner (and manager) of a firm with productive investment opportunities. They have no access to capital markets and therefore finance all consumption with payouts from the firm (production that is not reinvested). Lastly, the decision maker (and firm) live for two dates (i.e., the setting in the Production section in the lecture notes): - Pt=F(Kt1) is the $ value of production in at time t. - F(Kt1) is the production function which describes how much output is generated at time t from capital Kt1 deployed at at time t1. Remember, it takes time to produce. - P1=F(K0) is given (comes from time 0 ). P2=F(K1) is determined by capital deployed in time 1. - Production can be converted into capital and reinvested or used for consumption of the composite good (at no cost). - Le., production is either i) consumed or ii) reinvested into the production process. - It= capital invested into production at time t. I1= capital invested at time 1. I2=0= capital invested at time 2 . - Kt= capital deployed at time t. - Capital depreciates at a rate of =1 per period. - At t=1 the decision maker carries forward K0(1) in capital from the prior date (effectively endowed to the decision maker). - At t=2 the decision maker carries forward K1(1) from t=1. - Ct= consumption of the composite good at time t. C1= consumption at time 1 . C2= consumption at time 2 . - Lifetime utility: U(C1,C2)=u(C1)+u(C2) QUESTION 3. PRODUCTION WITH NO EXCHANGE 4 Part A: Derive and interpret the intertemporal budget constraint. A few quick sentences should be sufficient. Part B: Write down the individual's optimization problem. Part C: Derive the first-order conditions. Part C: Discuss the problem of multiple owners in this setting and explain how Fisher's separation theorem addresses this problem. Put differently, how does incorporating capital markets into the analysis address the issue that arises with multiple owners in a setting with production only. You can use a figure in your explanation if you'd like but do not need to make any calculations