 # Model Applications and Economics

## Question

1. A zero-coupon bond is one where the issuer pays no coupons, but pays a single cash-flow at the maturity of the bond. Assume you have 10-year zero-coupon bond that pays \$1,000 at maturity. Assume that the nominal rate of the bond over the next 10 years is constant at 5%, while the inflation rate is 2%.
a) What is the current value of the bond using the nominal interest rate?
b) What is the current value of the bond using the real interest rate as estimated using the Fisher relation approximation?

2. Assume you just deposited \$1,000 into a bank account. The current real interest rate is 2% and inflation is expected to be 6% over the next year.
a) What nominal interest rate would you require from the bank over the next year?
b) How much money will you have at the end of one year?
c) If you are saving to buy a stereo that currently sells for \$1,050, and assuming that the price of the stereo increases at the rate of inflation, will you have enough to buy it?

3. Suppose you are given the utility function U(C, l) = lnC + 2l, where C = consumption and l = leisure, and the production function Y = zK⁰.⁴N⁰.⁶.
Assume that all output is consumed (Y = C), and that hours of leisure/work are normalized as representing fractions of a day (or equivalently, a value of 1 represents 24 hours).
Suppose z = 1 and K = 20.
a) What are the Pareto-optimal hours of work?
b) What are the Pareto-optimal hours of leisure?
c) What is the Pareto-optimal level of output?

4. Given the efficiency wage function:
e(w) = w⁴ – 18w³ + 96w²
What is the optimal wage that the firm should set?

5. Given the production function, Y = zF(K, N) = zKαNβ, what conditions on α and/or β are necessary to achieve the multiple equilibria result as implied by the Keynesian Coordination Model?

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