A review of industry-wide data for the domestic wine manufacturing industry suggests the following industry supply function:
Q = -7,000,000 + 400,000P - 2,000,000PL - 1,500,000PK + 1,000,000W
Where Q is cases supplied per year, P is the wholesale price per case ($), PL is the average price paid for unskilled labor ($), PK is the average price of capital (in percent), and W is weather measured by the average seasonal rainfall in growing areas (in inches).
A. Determine the industry supply curve for a recent year when P = $80, PL = $10, PK = 12%, and W = 25 inches of rainfall. Show the industry supply curve with quantity expressed as a function of price and price expressed as a function of quantity.
B. Calculate the quantity supplied by the industry at prices of $50, $75 and $100 per case.
C. Calculate the prices necessary to generate a supply of 10 million, 25 million, and 50 million cases.