Question

Q2. Consider the general supply function:

Q_s = 1,000 + 20 P - 9 P_I +25 F

Q_s = quantity supplied

P = price of the commodity

P_I = 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 P_I = $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.

Answer 1

b. QS = 1,000 + 20 P - 9 P_I +25 F

Given: P_I = $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