The generalized demand and supply functions for good X are Qx d = 100 – 2 P X +
ID: 1225145 • Letter: T
Question
The generalized demand and supply functions for good X are
Qxd = 100 – 2PX + 0.01M + 8 PY - 4Pz Qxs = 50 + 3PX – 6PI + PT
Where
QXd= quantity demanded of good X
Px = price of good X
M = consumer income
PY = price of good Y
Pz= price of good Z
QXs= quantity supplied of good X
Px = price of good X
PI = price of input I
PT= price of technology T
a. Does the Law of Demand hold in this demand equation? How do you know?
b. Does the Law of Supply hold in this supply equation? How do you know?
c. Are good X and good Y substitutes or complements? How do you know?
d. Are good X and good Z substitutes or complements? How do you know?
e. Is good X a normal good or an inferior good? How do you know?
f. What is the demand function when M = $2,000, PY = $10 and PZ = $5?
g. What is the supply function when PI = $10 and PT = $20?
h. Solve for the equilibrium price (Po) and the equilibrium quantity (Qo).
i. Find the inverse demand function.
j. Find the inverse supply function.
k. Sketch the graph of this market.
l. Suppose that incomes increase to $2,500. Solve for the new equilibrium price (P1) and the new equilibrium quantity (Q1).
Where
QXd= quantity demanded of good X
Px = price of good X
M = consumer income
PY = price of good Y
Pz= price of good Z
QXs= quantity supplied of good X
Px = price of good X
PI = price of input I
PT= price of technology T
Explanation / Answer
(a) Yes, law of demand holds, since the coefficient of own price in the demand function is negative, signifying as own price increases (decreases), quantity demanded decreases (increases).
(b) Yes, law of supply holds, since the coefficient of own price in the supply function is positive, signifying as own price increases (decreases), quantity supplied increases (decreases).
(c) Goods X & Y are substitutes, since coefficient of price of Y in demand function is positive, signifying that as price of Y increases (decreases), demand for X increases (decreases).
(d) Goods X & Z are complements, since coefficient of price of Z in demand function is negative, signifying that as price of Z increases (decreases), demand for X decreases (increases).
(e) X is a normal good, since coefficient of income in demand function is positive, signifying that as income increases (decreases), demand for X increases (decreases).
(f)
Qxd = 100 – 2PX + 0.01M + 8 PY - 4Pz = 100 - 2PX + (0.01 x 2,000) + (8 x 10) - (4 x 5)
Qxd = 100 - 2PX + 20 + 80 - 20
Qxd = 180 - 2PX
NOTE: First 6 sub-parts are answered.
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