Suppose there are a fixed number of 1,000 identical firms in the perfectly competitive concrete pipe industry. Each firm produces the same fraction of total market output and each firm's production function for pipe is given by
q = √KL
and for this production function
RTS (L for K) = K/L
Suppose also that the market demand for concrete pipe is given by
Q = 400,000 – 100,000P
Where Q is total concrete pipe.
a. If w = v = $1, in what ratio will the typical firm use K and L? What will be the long-run average and marginal cost of pipe?
b. In the long-run equilibrium, what will be the market equilibrium price and quantity for concrete pipe? How much will each firm produce? How much labor will be hired by each firm and in the market as a whole?
c. Suppose the market wage, w, rose to $2 while v remained constant at $1. How will this change the capital-labor ratio for the typical firm, and how will it affect its marginal costs?
d. Under the conditions of part c, what will the long-run market equilibrium be? How much labor will now be hired by the concrete pipe industry?
e. How much of the change in total labor demand from part b to part d represents the substitution effect resulting from the change in wage and how much represents the output effect?