Assignemnt

1. Consider an economy inhabited by overlapping generations of two-period-lived individ- uals, each of whom receives an endowment of y in the first period of life and none in the second. The population of newborns grows as follows: N_t = nN_t-1, where n > 1. The money stock (the only asset in this economy) is constant.

(a) Find the equation for the budget set of an individual in the monetary equilibrium. Graph it. Show an arbitrary indifference curve tangent to the budget set and indicate the levels of consumption c₁ and c₂ that would be chosen by an individual in this equilibrium.

(b) On the figure from part a, draw the feasibility line. Label your graph carefully, distinguishing between the budget and feasibility constraints.

(c) Does the monetary equilibrium maximize the utility of future generations? Sup- port your assertion with references to your figure.

2. Assume that fiat money and capital are perfect substitutes as assets and that individ- uals wish to hold the one with a higher rate of return, but that it takes time to adjust capital holdings. In equilibrium individuals hold both assets. The real rate of return on money is n/z , where n = 1 and z = M_t / M_t-1. The gross real rate of return on capital is f' (k_t) = 100 / k_t.

Mt-1

(a) What is the equilibrium level of capital when the money stock is constant? What is it when the money stock is doubled in every period?

(b) What is the equilibrium nominal rate of return when the money stock is constant? What is it when the money stock is doubled in every period?

(c) What are the immediate and long-run effects on capital holdings of an unantici- pated increase in the growth rate of the money stock?

(d) What does this model predict for the relationship between inflation and output? Does it matter whether inflation is anticipated or not?

(e) How does your answer in part d differ from what the Lucas model predicts?

3. Consider an overlapping-generations model with inside and outside money, where the rate of return on inside money is x, while the rate of return on outside money is 1 . There is a one-time transaction cost of φ associated with inside money, independently of the purchase size.

(a) Show graphically how individuals optimally decide whether to use inside or outside money depending on the size s_i of their purchase. Show who uses inside money and who uses outside money.

(b) What is the effect on the deposit-to-currency ratio, nominal money stock M1 and present and future GDP of an anticipated increase in z (anticipated inflation)?

(c) How would your answer in part b differ if the increase in z was unanticipated (unanticipated inflation)?

(d) How could this model explain positive co-movement between M1 and GDP with- out ever-increasing inflation?