There are 2 firms in the market and each of them plans the

Question

There are 2 firms in the market and each of them plans the production as Q = K^1/3L^1/3, where K is capital and L labor. Given K=8, capital rental rate R=0.5, and wage W=8, answer the following questions if the market demand function is Q = (P+2)^1/2

1. What is the supply relation by a firm?

2. What is the labor demand relation by a firm?

3. Can you derive the variable cost of a firm?

4. What is the total cost of a firm?

5. What is the cost of producing more units of good?

6. In equilibrium, what is the supply function of a firm?

7. What is the total supply function of the economy?

8. What is the equilibrium price for goods?

9. What is the equilibrium quantity of goods?

10. How much labor will a firm demand?

11. What is the revenue of a firm?