Question #268165

Suppose the demand curve for a product is given by Q = 300 – 2P + 4I, where I is average income measured in thousands of dollars. The supply curve is Q = 3P – 50.

a. If I = 30, find the market clearing price and quantity for the product.

b. If I = 60, find the market clearing price and quantity for the product.

c. Draw a graph to illustrate your answers.



1
Expert's answer
2021-11-18T10:40:08-0500

a. Given that I=30I=30

Then the demand curve Q=3002P+4(30)Q = 300 – 2P + 4(30)

or Q=4202PQ = 420-2P


To find marketing clearing price, demand should be equal to supply

Qd=QsQ_d =Q_s


4202P=3P50420−2P = 3P – 50


5P=4705P = 470


P=94P = 94


Therefore


Q=4202(94)Q=420−2(94)


Q=420188Q=420- 188


Q=232Q =232


b. Given that I=60I=60

Then the demand curve Q=3002P+4(60)Q = 300 – 2P + 4(60)

or Q=5402PQ = 540-2P


To find marketing clearing price, demand should be equal to supply

Qd=QsQ_d =Q_s


5402P=3P50540−2P = 3P – 50


5P=5905P = 590


P=118P = 118


Therefore


Q=5902(118)Q=590−2(118)


Q=590236Q=590- 236


Q=354Q =354


c.






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