Supply Function
A review of industrywide data for the jelly and jam manufacturing industry suggests the following industry supply function:
Q = -59,000,000 + 500,000P - 125,000PL
- 500,000PK + 2,000,000W
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 PL = $8, PK = 10 percent, and W = 20 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, $60, and $70 per case.
C. Calculate the prices necessary to generate a supply of 4 million, 6 million, and 8 million cases.