Optimal Supply

Essay

Optimal Supply. Shake-n-Shing, Inc., is a supplier of wood shakes and shingles used in home construction. Shakes and shingles are sold by the bundle. Based on an analysis of monthly cost and output data, the company has estimated the following relation between its marginal costs and monthly output:

A. Calculate marginal cost at 500,000, 700,000, and 900,000 bundles of output.
B. Express output as a function of marginal cost. Calculate the level of output at which MC = $75, $100 and $125.
C. Calculate the profit-maximizing level of output if prices are stable in the industry at $100 per bundle, and, therefore, P = MR = $100.
D. Again assuming prices are stable in the industry, derive Shake-n-Shing's supply curve for bundles of shakes and shingles. Express price as a function of quantity and quantity as a function of price.