b) Assuming that PL (the price of labour) is equal to $8 and PK (the price of c

b) Assuming that PL (the price of labour) is equal to $8 and PK (the price of capital) is equal to $32 find the equation for the short-run total cost (as a function of output) SR TC. Neatly show your calculations. c) What is short run marginal cost function SR MC (as a function of output). Neatly show your calculations. d) Assuming this firm is perfectly competitive and the market price in the short run is: P = $30 how many units of output should this firm produce? What quantity of labour should the firm hire? What are total profits in the short run? Now we move to the long run where both L and K are variable. The Marginal Rate of Technical Substitution for the production function is:
e) Given this MRTS and assuming that PL is the price of labour and that PK is the price of capital find the cost minimizing quantity of Labour and Capital. Your solutions for L and K are called the conditional input demand functions and both are functions of output and the input prices. That is: L*(q PL PK) = ? And K*(q PL PK) = ? . You are to solve in general terms for this question which means you do not plug in specific values for q PL and PK . There are two ways to solve this question. You can use the two equations that represent the cost minimizing conditions to solve for your two unknowns. Or you can minimize total cost with the production function as your constraint. f) Assuming that PL = $8 and PK = $32 if the firm expects to continue to produce the same quantity of output that you indicated in your answer to part d) what quantity of labour and capital should the firm plan hire to minimize the cost of production?