Answer to Question #101979 in Microeconomics for Promith

Question

Consider the general supply function:
Qs 5 60 1 5P 2 12PI 1 10F
where Qs 5 quantity supplied, P 5 price of the commodity, PI 5 price of a key input in
the production process, and F 5 number of firms producing the commodity.
a. Interpret the slope parameters on P, PI
, and F.
b. Derive the equation for the supply function when PI 5 $90 and F 5 20.
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 $300 and $500

Answer 1

Answer on #Q101952

Question.

Consider the general supply function:

Qs 5 60 1 5P 2 12PI 1 10F

where Qs 5 quantity supplied, P 5 price of the commodity, PI 5 price of a key input in

the production process, and F 5 number of firms producing the commodity.

a. Interpret the slope parameters on P, PI

, and F.

b. Derive the equation for the supply function when PI 5 $90 and F 5 20.

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 $300 and $500

Solution.

a) A. Qs = 60 + 5P -12P1 + 10F

We have indicating that Qs will increase 5 if P increases by 1.

indicating that Qs decreases by 12 if P1 increases by 1.

indicating that Qs increases by 10 if F increases by1.

B. P1 = 90, F = 20

Putting in the given supply function, we get

Qs= 60+5P -12*90+10*20

= 5P - 820

C. Plot of Qs v/s P is given below.

Where Qs intersects price axis, we will have Qs = 0.

Hence, 0 = 5P-820 or P =820/5 = 164.

When price is 164, supply will be zero. If price goes below this, there will be no supply. It means that it is the minimum price at which a firm will like to supply.

D. We have Qs = 5P-820.

For getting inverse function, we express P as function of Q.

We have

For Qs = 680, we have

It indicates that maximum supply can be 680 units at the price of 300.