16. Suppose that the generalized demand function for good X is Qd = 60 - 2Px + 0

Question

16. Suppose that the generalized demand function for good X is
Qd = 60 - 2Px + 0.01M + 7Pr

where
Qd = quantity of X demanded
Px = price of X
M = (average) consumer income
Pr = price of a related good R

a. Is good X normal or inferior? Explain.
b. Are goods X and R substitutes or complements? Explain.
Suppose that M = $40,000 and Pr = $20.
c. What is the demand function for good X?
Suppose the supply function is
Qs = -600+10Px
d. What are the equilibrium price and quantity?

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

f. What happens to equilibrium price and quantity if other things remain the same as in part d but the price of good R decreases to $14?

g. What happens to equilibrium price and quantity if other things remain the same, income and the price of the related goods are at their original levels, and supply shifts to Qs = -360+10Px?

Explanation / Answer

Qd = 60 - 2Px + 0.01M + 7Pr

where
Qd = quantity of X demanded
Px = price of X
M = (average) consumer income
Pr = price of a related good R

a. Is good X normal or inferior? Explain.

Ans : Normal good ; Because Demand for good increase as income M increases.

b. Are goods X and R substitutes or complements? Explain.

Ans : Substitues of Each other . Because Increase in price of R Increase demand of X

Suppose that M = $40,000 and Pr = $20.
c. What is the demand function for good X?

Ans :Qd = 600 - 2Px

Suppose the supply function is
Qs = -600+10Px

d. What are the equilibrium price and quantity?

Ans : Qd= Qs ;

600 - 2P = - 600 +10P

1200 = 12P

P = $100

Q = 400


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

Ans

Qd = 720 - 2P

Qs = -600 + 10P

Qd = Qs

1320 = 12 P

P = $110 ;

Q = 500;

f. What happens to equilibrium price and quantity if other things remain the same as in part d but the price of good R decreases to $14?

Ans

Qd = 558 - 2P

Qs = -600 +10 P

1158 = 12 P

P= $96.5

Q =365

g. What happens to equilibrium price and quantity if other things remain the same, income and the price of the related goods are at their original levels, and supply shifts to Qs = -360+10Px?

Qd = 600 - 2P

Qs = -360 +10P

Qd = Qs

960 = 12P

P = $80

Q = 440

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