Question 1. An economy has full-employment output of Y= 1850. Desired consumption and desired investment are
C 500 0.5(Y - 7)-100, =400-100r
Government purchases and taxes are G = T = 200. Money demand is
M° P(0.5Y - 200i).
The nominal money supply is M = 3560. The expected inflation rate is .' -0.05.
(a) What are the general equilibrium values of the real interest rate, the price level, consumption, and investment?
(b) Suppose the desired investment function changes to
= 350 -100r.
What are the new general equilibrium values of the real interest rate, the price level, consumption, and investment?
Question 2. Use the IS-LM-FE graphical model, with accompanying explanation, to determine the effects of a decrease in wealth as follows.
(a) Determine the effect, in comparison to the initial general equilibrium, on the equilibrium values of the real wage, employment, output, real interest rate, consumption, private saving, investment, and the price level in short-tun equilibrium.
(b) In this part of the question, proceed with the comparison of the new general equilibrium to the initial general equilibrium. That is, determine the effect of the shock on the equilibrium values of the real wage, employment, output, real interest rate, consumption, investment, private saving, and the price level, where "equilibrium values" refers to values in the new general equilibrium in comparison to the initial general equilibrium.
Answer this question assuming for the sake of simplicity that the shock has no impact on current labor supply, current labor demand, the current level of the capital stock, or the current productivity coefficient, and no (direct) impact on money demand.
Make use of the framework covered in class. This framework is sot out in Handout 11 and Handout 11 -Addendum.
Question 3. Numerical Problem
An important lesson to be gained from this exercise is that the current state of the business cycle may be, at least in part, a result of the accumulation of a sequence of (possibly) small shocks occurring over the last three or four years.
To get credit for this question, you mug include a carefully drawn graph showing your results, along with an answer to the book's question regarding description of cycles. The graph must be clearly scaled with line segments connecting the points.
Q4. Numerical Problem 4. (b), (c), p.439, but with the following changes and suggestions. (i) Make use of our usual IS-LM-FE model for this question. Ignore the AD-AS model. (ii) Assume that the expected inflation rate is zero (already implicit in the set-up of the question). (iii) Solve part (c) in the usual wayrIong-run equilibrium" here means "general equilibrium"), paying close attention to the entire set of variables for which values are needed.
6. Try the following experiment: Flip a coin fifty times, keeping track of the results. Think of each "heads" as a small positive shock that increases output by one unit; similarly, think of each "tails" as a small negative shock that reduces output by one unit. Let the initial value of output, Y, be 50, and graph the level of output over time as it is hit by the "positive" and "negative" shocks (coin flips). For example, if your first four flips are three heads and a tail, out¬put takes the values 51, 52, 53, 52. After fifty flips, have your small shocks produced any large cycles in output?
7. In a particular economy the labor force (the sum of employed and unemployed workers) is fixed at 4. An economy is described by the following equations:
Desired consumption Cd = 300 + 0.5(Y - 7) - 300r.
Desired investment Td =
100
- 1001.
Government purchases G =
100.
Taxes T =
100.
Real money demand L =
0.5Y
- 200r.
Money supply M =
6300.
Full-employment output Y =
700.
a. Write the equation for the aggregate demand curve. (Hint: Find the equations describing the goods market and asset market equilibria. Use these two equations to eliminate the real interest rate. For any given price level, the equation of the aggregate demand curve gives the level of output that satisfies both goods market and asset market equilibria.)
b. Suppose that P = 15. What are the short-run equilibrium values of output, the real interest rate, consumption, and investment?
c. What are the long-run equilibrium values of output, the real interest rate, consumption, investment, and the price level?