Question

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.

Answer 1

a. Given that $I=30$

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

or $Q = 420-2P$

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

$Q_d =Q_s$

$420−2P = 3P – 50$

$5P = 470$

$P = 94$

Therefore

$Q=420−2(94)$

$Q=420- 188$

$Q =232$

b. Given that $I=60$

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

or $Q = 540-2P$

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

$Q_d =Q_s$

$540−2P = 3P – 50$

$5P = 590$

$P = 118$

Therefore

$Q=590−2(118)$

$Q=590- 236$

$Q =354$

c.