Suppose a firm’s production function is given by Q = L^1/2*K^1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by:
MPL = (K^1/2)/(2L^1/2), and MPK= (L^1/2)/(2K^1/2) .
a) If the price of labor is w = 36, and the price of capital is r = 64, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q = 24?
b) What is the firm’s Total Cost function TC(Q)?
c) What is the firm’s marginal cost of production?
3. Suppose in the short run a perfectly competitive firm has variable cost = 3q2, and MC = 6q where q is the quantity of output produced. Also, the firm has fixed cost F = 2500.
a) If the market price of the product is 270, how much output should the firm produce in order to maximize profit?
b) How much profit will this firm make?
c) Given your answer to b), what will happen to the market price as we move from the short run to the long run?
4. Suppose honey is produced in a beehive using bees and sugar. Each honey producer uses one beehive which she rents for $1/month. Producing q gallons of honey requires spending q dollars on bees, and q2 dollars on sugar.
a) What is the total cost of producing q units of honey for an individual honey producer?
b) What is the average cost of producing q units of honey per month for an individual producer?
c) In general, if the total cost of producing honey is a + bq + cq2, then the marginal cost of producing honey is b + 2cq. Assuming each honey producer operates as a price-taker, what is the supply curve for an individual producer?
d) Let Q be the total market supply, and q is the supply of an individual firm. Therefore, q = Q/n where n is the total number of firms in the market. Determine an expression for the market supply curve.
e) Suppose the demand for honey is given by Q = 45-P. Also, suppose there are 20 honey producers in the market. What is the equilibrium price of honey?
f) How much profit does an individual producer make? Is this a long run equilibrium?