1 Question 1 Consider a represenatitive consumer whose utility can be summarized by the lifetime utility function B+ log ct t Stocks held at the beginning of period t pay a dividend Dt. Denote stock prices by St and the asset position of the individual at the beginning of period t by at-1.Individuals pay sales tax on their consumption at the rate t each period. The price of the final good is denoted by Pt and individual income each period is Yt. (a) Write down the budget constraint for the representative consumer in periond t (b) Write down the sequential Lagrangian and derive the first order condi- tions for consumption at time t, time t +1 and the choice of asset position at time t, at (c) Derive the pricing kernel (d) Suppose the sales tax in period t+1 increases. What effect will this have on stock prices in period t? Give both mathematical and intuitive reasons for your answer. 1 Question 1 Consider a represenatitive consumer whose utility can be summarized by the lifetime utility function B+ log ct t Stocks held at the beginning of period t pay a dividend Dt. Denote stock prices by St and the asset position of the individual at the beginning of period t by at-1.Individuals pay sales tax on their consumption at the rate t each period. The price of the final good is denoted by Pt and individual income each period is Yt. (a) Write down the budget constraint for the representative consumer in periond t (b) Write down the sequential Lagrangian and derive the first order condi- tions for consumption at time t, time t +1 and the choice of asset position at time t, at (c) Derive the pricing kernel (d) Suppose the sales tax in period t+1 increases. What effect will this have on stock prices in period t? Give both mathematical and intuitive reasons for your