Question

The Long Run Economy

a)   An economy has a savings rate of s = 0.2 and capital depreciates at a rate of δ=0.1. Output is produced using the production function:

?(?) = ?√(?)(?),

Where Y(t) is GDP, K(t) is the capital stock, L(t) is the number of workers. TFP A has the value of A=2. Assume that the working population is constant in size.

a) What will GDP per capita in the economy be in the long run (steady state)?

b)   In this same economy where s=0.2, what is the consumption function in this economy (i.e., what is consumption as a function of income)?

c)   If there is no government spending or taxation in this economy what is the real interest rate r in the long run (steady state) if the investment function is

? = 3.6 − 8?.

d)   What is inflation π in the long run (steady state) if the supply of money grows at 5% a year?

e)   What is the nominal interest rate i in this economy in the long run?

f) What is the long run (steady state) frictional unemployment rate in this economy if unemployed workers have a 97% chance of finding a job each month and 3% of workers separate from their jobs each month?

Answer 1

At the steady state, the natural rate of unemployment is

Therefore, the frictional unemployment rate at the steady state is 3%.