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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

Expert verified

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

01

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.

02

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.

03

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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In 2010, Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The average retail price (including taxes) was about \(5.00 per pack. Statistical studies have shown that the price elasticity of demand is -0.4, and the price elasticity of supply is 0.5.

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