P3.7 Supply Function: A review of industry-wide data for the jelly and jam manuf
ID: 1248336 • Letter: P
Question
P3.7 Supply Function: A review of industry-wide 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.
Explanation / Answer
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.
Qs = -59,000,000 + 500,000P – 125,000PL – 500,000Pk + 2,000,000W
= -59,000,000 + 500,000P – 125,000 ($8) – 500,000(10) + 2,000,000 (20)
= -59,000,000 + 500,000P – 1,000,000 – 5,000,000 + 20,000,000
= -65,000,000 + 20,000,000 + 500,000P
Qs = - 25000000 + 500,000P
500000P= Q +25000000
P= Q/500000 + 25000000/500000
P= $50 + $0.000002Q
By substituting the Price is Qs equation we get the quantity supplied at respective price levels
At, P= $50
Qs= - 25000000 + 500,000P
=- 25000000 + 500,000 (50)
= - 25,000,000 + 25,000,000
Qs= 0 units
At, P= $60
Qs= - 25000000 + 500,000P
=- 25000000 + 500,000 (60)
= - 25,000,000 + 30,000,000
Qs= 5,000,000 units
At, P= $70
Qs= - 25000000 + 500,000P
=- 25000000 + 500,000 (70)
= - 25,000,000 + 35,000,000
Qs= 10,000,000 units
C. Calculate the prices necessary to generate a supply of 4 million, 6 million, and 8 million cases.
By substituting the quantity supplies in the inverse supply equation we can find the price that can be charged at different levels of supply.
Inverse supply equation:
P= $50 + $0.000002Q
When supply is 4millions, Price is equal to:
P= $50 + $0.000002 (4 millions)
=$50 + $0.000002 (4,000,000)
= $50 + $8
= $58
P= $58
When supply is 6millions, Price is equal to:
P= $50 + $0.000002 (6 millions)
=$50 + $0.000002 (6,000,000)
= $50 + $12
= $62
P= $62
When supply is 8millions, Price is equal to:
P= $50 + $0.000002 (8 millions)
=$50 + $0.000002 (8,000,000)
= $50 + $16
= $66
P= $66
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