Suppose there are 1,000 identical firms producing diamonds and that the short-run total cost curve for each firm is given by
STC = q2 + wq
and short-run marginal cost is given by
SMC = 2q + w
where q is the firm’s output level and w is the wage rate of diamond cutters.
a. If w = 10, what will be the firm’s (short-run) supply curve? What is the industry’s supply curve? How many diamonds will be produced at a price of 20 each? How many more diamonds would be produced at a price of 21?
b. Suppose that the wages of diamond cutters depend on the total quantity of diamonds produced and the form of this relationship is given by
w = .002Q
Where Q represents total industry output, which is 1,000 times the output of the typical firm. In this situation, show that the firm’s marginal cost (and short-run supply) curves depends on Q. What is the industry supply curve? How much will be produced at a price of 20? How much more will be produced at a price of 21? What do you conclude about how the shape of the short-run supply curve is affected by this relationship between input prices and output?