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Magazine Chapter 2: Q1. (page 84)
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.
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