1. Assume an economy has a production function of:
Y = AK
.35L
.65 with: A = 100, K = 1,000 and L = 400. There is no labor force growth and technology remains constant.
(a) Assume that the capital stock in this economy depreciates at 10%/year and the savings rate out of GDP is 40%. What would be the steady state level of y, c, s, k?
(b) Derive the golden rule savings rate for this economy. (Hint it will be 35 percent) What would be the new level of steady state y, c, s, k if the economy moved to the golden rule savings rate?
2. Using the same production function as in question 1 assume that total GDP (Y) is growing 4 percent per year, the labor force (L) is growing 1.5 percent per year, and the capital stock (K) is growing 3 percent per year. How fast (by what percent) is total factor productivity (A) growing per year? How fast is output per worker (Y/L) growing, and what is the contribution of the growth of total factor productivity growth (dA/A) to that growth? What is the contribution of a faster rate of capital growth compared to labor force growth a[dK/K – dL/L] to increases in Y/L?
(Remember these are large letters)
3. Taylor Rule
Assume an economy with an AE curve with a slope of 1 where a one percent change in real interest rates changes real GDP by 1 percent with a one year lag; and a slope to the short run Phillips curve of 1 where a 1 percentage point increase in real GDP increases inflation by 1 percent, also with a one year lag. From Okun’s law for this economy a 1 percent change in real GDP changes the unemployment rate by .5%. The natural rate of unemployment for this economy is 5%. The neutral real rate of interest r
n = 3.0 %/ and the target rate of inflation ?t = 2%.
Assumes that policy makers inherit an economy at its natural rate of unemployment (5%), 6 percent inflation, and decide to use a hard Taylor rule of:
r = 3% XXXXXXXXXXoutput gap) + 1.0 (? – 2%)
Fill in the following table assuming that policy makers have a correct model of the economy, follow the Taylor rule, and the economy has the two one period lags. Remember that in each year the policy choice for the real interest rate changes. (Your policy choice in year 0 affects GDP in Y in year 1 and how that policy affects GDP in year 1 affects inflation in year 2.
Hint. Use the Taylor rule to pick r in period 0 based on information in table. That r chosen for year 0 will have an impact on Y (and u based on Okun’s law) in year 1, but will have no impact on inflation until year 2 depending on the output gap that opens up in year 1.
Year Policy Choice for r Y ? u
XXXXXXXXXX
1 6
2
3
4