A producer has the following technology.y= 6K^(1/2)L^(1/2) a) Prove formally that the production function exhibits constant returns to scale (use “λ” argument). b) Find analytically MPL and MPK. Is MPL increasing, decreasing, or constant inL? Is MPK increasing, decreasing, or constant in K? c) Short-run: Given stock of capital ̄K= 1 find labor demand (formula) of a competitive firm. Find equilibrium real wage rate if labor supply is given by Ls= 9 (one number).

A producer has the following technology.y= 6K^(1/2)L^(1/2)

a) Prove formally that the production function exhibits constant returns to scale (use “λ” argument).

b) Find analytically MPL and MPK. Is MPL increasing, decreasing, or constant inL? Is MPK increasing, decreasing, or constant in K?

c) Short-run: Given stock of capital ̄K= 1 find labor demand (formula) of a competitive firm. Find equilibrium real wage rate if labor supply is given by Ls= 9 (one number).

d) Assume again ̄K= 1 and that Ls= 9. The government adopts a real minimum wage of wmin/p=(3/2). Find labor demand (one number) and the unemployment rate (one number). Please depict the equilibrium on a graph with the real wage on the vertical axis and labor on the horizontal axis, indicating the equilibrium quantity of labor, wage, and unemployment, as well as the relevant curves.

e) Find the cost function given prices of inputs wK= 4 and wL= 1 (formula). Plot the cost function on a graph, indicating the slope of the cost curve.

f) Write down the two conditions for profit maximization in the long run. Provide their economic intuition (two equations and two sentences). Demonstrate that the two conditions imply the cost-minimization condition (for the profit-maximizing level of output).