Question

Suppose the demand curve for a product is given byQ= 300 - 2P+ 4I, whereIis average income measured in thousands of dollars. The supply curve isQ= 3P- 50.

a. IfI= 25, find the market-clearing price and quantity for the product.

b. IfI= 50, find the market-clearing price and quantity for the product.

c. Draw a graph to illustrate your answers.

Short answer

a. The market-clearing price would be 90, and output would be 220.

b. The market-clearing price and output would be 110 and 180, respectively.

c. The graphical representation of the answers is as follows:

Step-by-step solution

Explanation for part (a)

If I=25, then

Demand:

Q = 300 - 2P + 4(25)

Q = 300 - 2P + 100

Q = 400 -2P

Supply: Q = 3P - 50

The market-clearing prices and quantity are determined where demand is equal to supply; therefore:

Q = S

400 -2P = 3P - 50

5P = 450

P = 90

Q = 400 - 2(90)

Q = 400 - 180

Q = 220

Therefore, the market price at I=25 would be 90, and the quantity would be 220.

Explanation for part (b)

If I=50, then

Demand:

Q = 300 - 2P + 4(50)

Q = 300 - 2P + 200

Q = 500 -2P

Supply: Q = 3P - 50

Since market clearing price and quantity will be determined at D=S, therefore:

Q = S

500 -2P = 3P - 50

5P = 550

P = 110

Q = 400 - 2(110)

Q = 400 - 220

Q = 180

Therefore, at I=50, the market-clearing price would be 110, and the quantity would be 180.

Explanation for part (c)

The graphical representation of parts (a) and (b) is as follows:

In both graphs, the y-axis depicts prices, and the x-axis depicts quantity demanded and supplied.

For part (a), D=S where the price is 90 and output 220. Similarly, for part (b), D=S, where prices are 110 and output, is 180.