Question
Q2. Consider the general supply function: Qs = 1,000 + 20 P - 9 PI +25...
Q2. Consider the general supply function:
Qs = 1,000 + 20 P - 9 PI +25 F
Qs = quantity supplied
P = price of the commodity
PI = price of a key input in the production process
F = number of firms producing the commodity
b. Derive the equation for the supply function when PI = $480 and F = 60. (1 point)
c. Sketch a graph of the supply function in part b. At what price does the supply curve intersect the price axis? Give an interpretation of the price intercept of this supply curve.
d. Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $1,000 and $1,500.
e. Derive the inverse of the supply function in part b. Using the inverse supply function, calculate the supply price for 40,000 units of the commodity. Give an interpretation of this supply price.
f. Suppose the supply curve for good X passes through the point P = $35, Qs = 2,500. Give two interpretations of this point on the supply curve.
Answers
b. QS = 1,000 + 20 P - 9 PI +25 F
Given: PI = $480 and F = 60
Substitute the values
QS = 1,000 + 20 P – 9(480) +25(60)
QS = 1,000 + 20 P – 4320 + 1500
QS = - 1820 + 20P
c. To find the intercept: Set QS = 0,
QS = - 1820 + 20P
0 = - 1820 + 20P
-20P = -1820
P = 1820/20
P = 91
Set P = 0 in QS = - 1820 + 20P
QS = - 1820 + 20(0)
QS = -1820
d. When P = $1000 and $1500, QS = ?
When P = $1000
QS = - 1820 + 20(1000)
QS = -1820 + 20000
QS = 18180
When P = $1000, QS = 18180
When P = $1500
QS = - 1820 + 20(1500)
QS = -1820 + 30000
QS = 28180
When P = $1500, QS = 28180
e. The inverse supply equation is P = 91+0.05Qs
Supply price for 40,000 units: P=91+0.05(40,000) = $2,091
The minimum price producers will accept to produce 40,000 units is $2,091.
f. 1. It indicates if price a good is $35, Quantity supplied is 2500 units. In other words, 2500 units is the maximum amount of product that sellers are willing and able to provide for $35.
2. If supply curve is QS = a + Pb
2500 = a + 35b
