Question

Suppose that the general demand function for good X is

Qd = 60 – 2Px 0.01M 7PR

where
Qd is quantity of X demanded,
Px is price of X,
M is average consumer income, and
PR is price of a related good R.

a)Is good X normal or inferior? Explain.

b)Are good X and R substitutes or complements? Explain.

c)Suppose that M = $40,000 and RR = $20. What is the demand function of good X.

d)Suppose the supply function is Qs = -600 10Px, what are the equilibrium price and quantity?

e)What happened to equilibrium price and quantity if other things remain the same as in part d) but income increases to $52,000?

Answer 1

Given,

a. The income elasticity of demand can be measured as follows

The coefficient of income (M) = 0.01.

Since, it is positive therefore, income elasticity of demand will also be a positive value. Hence, the good X is a normal good.

b. The coefficient of Pr is positive therefore the cross elasticity of demand will also be a positive value. Hence, the two goods X and R are substitute to each other.

c. M = $ 40,000 and Pr = $ 20

Plug in these values in the equation of demand, we get

Demand function, Qd = 600 - 2Px

d. Supply function, Qs = - 600 + 10Px

At equilibrium demand is equal to supply

600 - 2Px = - 600 + 10Px

=> 10Px + 2Px = 600 + 600

=> 12Px = 1,200

=> Px = $ 100

Q = 600 - 2 × 100 = 400 units

Equilibrium price = $ 100

Equilibrium quantity = 400 units

e. When income = $ 52,000

Equate demand to supply we get

720 - 2Px = - 600 + 10Px

=> 10Px + 2Px = 720 + 600

=> 12Px = 1,320

=> Px = $ 110

Q = 720 - 2 × 110 = 500 units

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