Subject: Microeconomics - Production Theory

Assume a firm operating under a production function:

f(x1,x2)=404x14x2

Suppose the price of input 1 is ₁, the price of input 2 is ₂, and the price at which the final good is sold is "".

Answer:

1) Explain what returns to scale are and show what returns to scale are like for this technology. 2) Explain and calculate what is the marginal productivity (MP) of input 1

3) Solve the profit maximizing firm problem to find the factor demands.

4) Replace the factor demands in the production function to find the level of production.

5) Now solved the firm's cost minimization problem, to find the conditional factor demand.

6) Find the cost function

7) Using the cost function you found above, solve the firm's profit maximization problem to find the supply function.

8) Verify that the production level you found in question (d) is the same as the supply function you found in question (g).

9) Assume that the price of input 1 is ₁ = 1, the price of input 2 is also ₂ = 1, and the price at which the final good is sold is = 100. Calculate the optimal level of production and verify that no matter which of the two problems you are solving ((be it (c) or (h)), in the end, the quantity of input 1 and input 2 demanded, and the level of production is the same.

** NOTE: in this case, I just need answers from question 4) to question 9)