Question

Consider the supply function: Qs = 60 + 5P – 12 PI + 10F , Where Qs = quantity supplied, P = price of the commodity, PI = price of a key input in the production process, and F = number of firms producing the commodity.

Interpret the slope parameters on P, PI, and F. 3 marks 

Derive the equation for the supply function when PI =$90 and F = 20. 1 mark

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. 6 marks            

Using the supply function from part b, calculate the quantity supplied when the price of the commodity is $300 and $500. 2 marks 

Derive the inverse of the supply function in part b. using the inverse supply function; calculate the supply price for 680 units of the commodity. Give an interpretation of the supply price.

Answer 1

Given,

$Q_s=60+5P-12PI+10F$

where,

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.

(a) Interpretation of the slope parameters is as follows:

• P: A $1 increase in the price of the commodity, keeping other things constant, causes the quantity supplied of the commodity to increase by 5 units.
• PI: A $1 increase in the price of the key input, keeping other things constant, causes the quantity supplied of the commodity to decrease by 12 units.
• F: Entry of an additional firm in the production of the commodity, keeping other things constant, causes the quantity supplied of the commodity to increase by 10 units.

(b) Given, PI =$90 and F = 20.

Putting the value of PI and F in the general supply function, we get the required supply function.

$Q_s=60+5P-12PI+10F$

$Q_s=60+5P-12(90)+10(20)$

$Q_s=5P-820$

Therefore, the supply function for the given values of PI and F is 

$Qs=-820+5P$

(c)

The supply curve is straight upward sloping line that intersects the price axis at $164 and the Quantity axis at -820 units. It is only the segment above the price of $164 that is economically meaningful.

The price intercept signifies the price below which the quantity will not be supplied, which in this case is $164.

(d)

When P=300,

$Q_s=-820+(5\times 2500)=680$

when p=500

$Q_s=-820+(5\times500)=1680$

(e)

$Q_s=-820+5P$

$5P=820+Q_s$

$P=164+0.2Q_s[inverse\space supply]$

When Qs = 680,

$When Qs = 680,$

$P = 164 + 0.2 x 680 = 164 + 136 = 300$

This supply price means that the producer will supply 680 units only when price of the good is 300 and above.