1) Consider two consumers, A and B. A and B both wish for perfect consumption smoothing (c = c^{f}) and both have no present wealth. Though, the two consumers have different income streams. Person A’s current income, y_{A}, = 100, and future income, y^{f}_{A}, = 121. Person B’s current income, y_{B}, is 120, and future income, y^{f}_{B}, = is 99. The real interest rate is 10%.
(a) Compute the current value of lifetime resources (PVLR) for consumer A and consumer B, respectively.
(b) Draw consumer A’s budget constraint. How does the budget constraint of consumer A compare to the budget constraint of consumer B? Describe
(c) Find consumer A’s most favourable lifetime consumption plan, (c_{A}, c^{f}_{A}). How does consumer B’s optimal lifetime consumption plan, (c_{B}, c^{f}_{B}), compare to consumer A’s lifetime consumption plan? Describe.
(d) Consumer A is a present saver or a present borrower? describe. Is consumer B a present saver or a present borrower? describe.
(e) Draw a graph which demonstrates how the increase in the interest rate (above 0.10) will affect the budget constraints of consumer A and consumer B. How does the budget constraint of consumer A compare to the budget constraint of consumer B?
2) Fred’s Frisbees is trying to find out how many Frisbee pressing machines to buy for its new factory. The real price of a new pressing machine is 7500 Frisbees. The depreciation rate on these Frisbee presses is equal to 10% per year. The expected future marginal product of these fabricating machines is given by the expression 3350 – 20K, measured in Frisbees. The real interest rate is 8% (.08).
(a) What is the user cost of capital?
(b) What is the profit-maximizing number of Frisbee presses for Fred’s to buy for its new factory?
(c) Before purchasing the machines Fred’s finds that it will be subject to a new tax of 32.5 percent on all of its revenue. Now what is the profit maximizing number of machines for Fred’s to purchase? (Round to the nearest whole number.)
3) Desired consumption for an economy is given by the equation
C^{d} = 1000 + .6Y – 4000r.
Government purchases are given by G = 1500.
(a) prepare the expression relating desired saving, S^{d}, to Y and r.
(b) Assume the full-employment level of output is 10,000. Graph the relationship between desired saving, S^{d}, and the real interest rate r. (graph must comprise properly labelled axes and an indication of scale on every axis.)
(c) If desired investment for a economy is given by the equation
I^{d} = 2000 – 6000r, compute the equilibrium real interest rate for the economy.
(d) Using the equilibrium real interest rate which you coputed in part (c), compute the equilibrium level of saving, investment, and consumption in the economy.
Does Y = C + I + G in equilibrium?
(e) Add the relationship between desired investment and the real interest rate to your graph in part (b), and show equilibrium values of r, S^{d} and I^{d} from parts (c) and (d)
4) Analyze the effects of each of the following on national saving, investment, and the real interest rate. describe your reasoning and illustrate it with an appropriate diagram.
(a) Consumer confidence falls, so consumers decide to consume less and save more at every level of the real interest rate.
(b) A new technology breakthrough increases the future marginal product of capital and expected future income.