I have the answers to these problems, but I would like further explanation of th
ID: 1092709 • Letter: I
Question
I have the answers to these problems, but I would like further explanation of the answers; specifically, can someone show me the math behind the answers?
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
a. Is good X normal or inferior? Explain.
Coefficient of M is positive, hence X is normal
b. Are goods X and R substitutes or complements? Explain.
Coefficient of Pr is positive, hence related good R is a substitute
Suppose that M = $40,000 and Pr = $20.
c. What is the demand function for good X?
demand function for good X = 60 - 2Px + 0.01*40000 + 7*20
Qd= 600-2Px
Suppose the supply function is
Qs = -600+10Px
d. What are the equilibrium price and quantity?
Qd=Qs
600-2Px= -600+10Px
Px= 100
Q= -600+10*100= 400
equilibrium price = $100
and quantity= 400 units
e. What happens to equilibrium price and quantity if other things remain the same as in part d but income increases to $52,000?
Qd= 60 - 2Px + 0.01*52000 + 7*20= 720-2Px
Qd= 720 -2Px= -600+10Px
Px= 110
Q= 720-2*110= 500
equilibrium price and quantity will increase
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?
Qd= 60 - 2Px + 0.01*40000 + 7*14= 558-2Px
Qs= -600+10Px
558-2Px=-600+10Px
Px= $96.5
Q= 558-2*96.5= 365
equilibrium price and quantity will decrease
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= 600-2Px
Qs = -360+10Px
Qd= Qs
600-2Px = -360+10Px
Px= 80
Q= 600-2*80= 440
equilibrium price will decrease and quantity will increase