Explain how a competitive profit maximizing firm decide how much of each factor of production to demand?

$[10$pts$]$

Write a Cobb$-$ Douglas production function describing an economy in which capital earns one fourth of total income? $[5$pts$]$

Suppose the production function in medieval Europe is $Y=A{K}^{0\mathrm{.}5}{L}^{0\mathrm{.}5},$ where $K$ is the amount of land and $L$ is the amount of Labor. Let's consider $A=1.$ The economy begins with $100$ unit of Land and $100$ unit of labor.

Find a numerical answer to each of the following questions $($Show your work$).$

$2+3=5pts$

a$)$ How much output does the economy produce?

b$)$ What are the wage $(W)$ and rental price of land $(K)?$

$4.$ Suppose that an economy production function $Y=A{K}^q{L}^{1-a}$ is Cobb$-$Douglas with parameter $=0\mathrm{.}3.$

a$)$ What fraction of income do capital and labor receive?

$[3$pts$]$

b$)$ Suppose that immigration increases the labor force by $10$ percent. What happens to total output in percentage? What happens to the real wage rate?

$6+6=12pts$

Define Marginal Propensity to Consume $($MPC$).$ Explain what happen to consumption when the government increases taxes?

$[5$pts$]$

Consider an Economy described as follows:

$Y=C+I+G$

$Y=8,000$

$G=2,500$

$T=2,000$

$C=1000+\frac{2}{3}(Y-T)$

$I=1200-100r$

a$)$ In this economy, compute private saving, public saving, and national saving.

$[6$pts$)\}$

b$)$ Find the equilibrium interest rate.

$[4$pts$]$