Assume that: 1) the person lives for two periods and works for the wage w₁ in period 1 and w₂ in period 2; 2) all sources of unearned income are zero in each period; 3) the person works a positive number of hours in each period; 4) lifetime utility is the sum of utility from each time period (and that utility in each time period has the same functional form as in question 1); 5) the interest rate and the the rate of time preference each equal zero; and 6) the price of consumption is 1 in each period.

A) Write out the person's two-period utility maximization problem.

B)Derive the first order conditions for the problem in part a).

C)Explain how the individual's problem would change if you assume the person cannot borrow money to fund period 1 consumption expenditure. Write out the new problem and specify the necessary conditions.

D)Using the necessary conditions from c), solve for a marginal rate of substitution condition between hours of work in period 1 and hours of work in period 2. Explain how it is affected by whether or not the person would like to be able to borrow in period 1.