1) In this problem we will find the labor demand and labor supply for an economy, from there we will determine the equilibrium quantity of labor, and by plugging that into the production function we will find GDP. Consider Robin Crusoe who has utility function: U(Y,L) = Y - L^2 /2 where Y is the output that Crusoe consumes, and L is labor hours Crusoe puts in.
Suppose in this economy firms only use capital and labor (K and L) as inputs to production, and they can make things with a technology represented by the production function: Y = 0.75 ln(K) + 0.25 ln(L) where “ln” is the natural log. So now keep in mind that you are trying to find Crusoe’s labor supply. Thus describe, mathematically, what do you have to do in order to find it? Go ahead and find the supply of labor. When you do, write in down - in nominal terms - in real terms.
d) Now that you have the Labor Demand and the Labor Supply, find the equilibrium: - nominal wage w*. - real wage ω*
e) Knowing this equilibrium wage, find now the equilibrium amount of labor in this economy: L*
f) Lastly suppose that the price level P is given by the CPI and that it is 100. Suppose also that the equilibrium amount of capital is known, and that it is
K* = 143.
Find the equilibrium level of output of this economy, both in nominal terms and in real terms. What is the level of unemployment?