4. Sang derives utility from consumption this year and next year, but dis- counts future utility by 8 according to: U(c1, c2) = In(ci) + Bin(c2) He earns income / today that is taxed at a payroll tax rate of tau, In period 2 he is retired and has no income, but he receives a social security payment S from the government, and anything he saved from period 1 earns a return r. a. What is Sang's budget constraint for c, and c2? b. Set up the expenditure minimization problem and solve for compen- sating demand for c, and c2. Hint: expenditures here are the present discounted value of consumption: c + 2 and the present dis- counted value of income is PDVI = /(1-7) + 75. Compensating demand functions here will be a function of utility level U, utility discount factor S, and return r. c. Find the substitution effect for ez if r increases. d. Find the optimal demand for c, and ez as a function of return r, discount factor B and PDV of income. c. By how much does optimal c2 change if r increases? d. Intuitively, explain the direction (positive or negative) of both the substitution effect and the income effect for both c, and c2 for the increase in r. c. What if they increase Sang's tax rate but his social security payment will increase by change in 7 times income, or Ar x /. Is Sang better off, worse off, or indifferent. Show why and explain