A firm uses labor and capital to produce output according to the production function q=100KL, where L is the number of units of labor used and K is the number of machines.
Suppose the price of capital is $120 per day and the price of labor $30 per day.
a) What is the marginal product of labor
b) What is the marginal product of capital
c) Using marginal product of inputs, find the firm’s marginal rate of technical substitution
d) What is the slope of isocost line?
e) Using the answer to (c) and (d), write down the tangency condition (the optimal choice condition) for this firm.
f) What is the minimum cost of producing 1000 units of output?