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Question 1 Consider a representative consumer who lives for ever and has a utility func- tion *$* (272+2 2/ Mt Pt t Each period, the consumer receives income Yz,and chooses his consumption Ct,money holdings Mt,risk free government bonds Bt,and stocks at. (a) What is the budget constraint in each period t? (b) Set up the sequential Lagrangian problem. (c) Derive the first order conditions for each of the consumer's choices. (d) Define the price kernel. Using this kernel, derive the stock pricing equa- tion and the bond pricing equation. (e) Derive the demand for real money as a function of consumption and the nominal interest rate. Mt Pt Question 1 Consider a representative consumer who lives for ever and has a utility func- tion *$* (272+2 2/ Mt Pt t Each period, the consumer receives income Yz,and chooses his consumption Ct,money holdings Mt,risk free government bonds Bt,and stocks at. (a) What is the budget constraint in each period t? (b) Set up the sequential Lagrangian problem. (c) Derive the first order conditions for each of the consumer's choices. (d) Define the price kernel. Using this kernel, derive the stock pricing equa- tion and the bond pricing equation. (e) Derive the demand for real money as a function of consumption and the nominal interest rate. Mt Pt

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