Question

Suppose the demand curve for a product is given by

?_? = 50 − 3?
and supply curve or this product is given by ?_? = 35 + 2?

(a) what is the equilibrium price and quantity?

(b) What is the price elasticity of supply at equilibrium? Is the price elasticity of supply elastic, inelastic or unit elastic? Explain your answer.

(c) What is the price elasticity of demand at equilibrium? Is the price elasticity of demand elastic, inelastic or unit elastic? Explain your answer.

(d) If a 20 percent increase in income leads to a 5 percent decrease in the demand for a good, the income elasticity of demand equals ________ and the good is ________ good.

(e) If a 5 percent increase in the price of good X leads to a 15 percent increase in the demand for good Y, and other things remain the same, the cross elasticity of demand equals ________and goods X and Y substitutes or complements?

Answer 1

a) At equilibrium,

QD = QS

50 - 3P = 35 + 2P

5P = 50 - 35 = 15

P = 15 / 5 = $3

Q = 50 - 3(3) = 41

Thus, the equilibrium price is $3 and quantity is 41 units.

b) Price elasticity of supply = (∆Q/∆P) * (P / Q)           [Where, ∆Q/∆P is price coefficient in supply function]

                                             = 2 * (3 / 41)

                                              = 0.15

Since Price elasticity of supply is less than 1, therefore, the price elasticity of supply is inelastic.

c) Price elasticity of demand = (∆Q/∆P) * (P / Q)           [Where, ∆Q/∆P is price coefficient in demand function]

                                             = -3 * (3 / 41)

                                              = -0.23

The absolute value of Price elasticity of demand is 0.23. Since Price elasticity of demand is less than 1, therefore, the price elasticity of demand is inelastic.

d) Income elasticity of demand = % change in demand / % change in income

                                                  = -5% / 20%

                                                  = -0.25

Since the income elasticity of demand is negative, the good is an inferior good.

If a 20 percent increase in income leads to a 5 percent decrease in the demand for a good, the income elasticity of demand equals -0.25 and the good is an inferior good.

e) Cross elasticity of demand = % change in demand for good Y / % change in price of good X

                                                  = 15% / 5%

                                                  = 3

Since Cross elasticity of demand is positive, goods X and Y are substitutes

If a 5 percent increase in the price of good X leads to a 15 percent increase in the demand for good Y, and other things remain the same, the cross elasticity of demand equals 3 and goods X and Y substitutes.