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Suppose that the general demand function for good X is Qd = 60 - 2Px + 0
Suppose that the general 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
i. Is good X normal or inferior? Explain. (1 mark)
ii. Are goods X and R substitutes or complements? Explain. (1 mark)
iii. Suppose that M = ¢40,000 and PR = ¢20. What is the demand function for good X? (2 marks)
Suppose the supply function is Qs = -600 + 10Px
iv. What are the equilibrium price and quantity? (3 marks)
v. What happens to equilibrium price and quantity if other things remain the same as in part (iv) but income increases to ¢52,000? (3 marks)
vi. What happens to equilibrium price and quantity if other things remain the same as in part (iv) but the price of good R decreases to ¢14? (3 marks)
vii. 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? (4 marks)
Expert Solution
i) Good x is a normal good
Reason: Normal goods means as income increases, the consumption of the good will also increase. Inferior goods means when income increases, the consumption of the good will decrease.
The given damand function is
Qd = 60 - 2Px + 0.01M + 7PR
In the demand function when M (income) increases, the quantity demanded (Qd) will also increase.
Therefore good x is a normal good
ii) Good X and R are substitutes.
Reason: Substitute goods means when the price of one good increases, the demand for other good will increase.
Complementary goods means when the price of one good increases, the demand for other good will decrease
The given demand function is
Qd = 60 - 2Px + 0.01M + 7PR
In the demand function, when price of good R (PR) increases, the quantity demanded (Qd) of good X will also increase
Therefore good x and R are substitutes
iii) M = 40,000
PR = 20
Therefore the demand function can be written as follows
Qd = 60 - 2Px + (0.01 *40,000) + (7 *20)
Qd = 60 - 2px + 400 + 140
= 60 -2Px + 540
= 600 - 2PX
The demand function for good x is
Qd = 600 - 2PX
??????iv) A market is in equilibrium when quantity demanded and quantity supplied become equal.
Qd = Qs
The demand function is
Qd = 600 - 2PX
The supply function is
Qs = -600 + 10PX
When Qd = Qs
600 - 2Px = -600 + 10Px
600 + 600 = 10Px + 2Px
1200 = 12 Px
Px = 1200 /12 = 100
Px = 100
To calculate quantity, substitute Px = 100 in 600 - 2Px
600 - 2 *100 = 400
Quantity = 400
The equilibrium price = 100
The equilibrium quantity = 400
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