Answer to Question #79597 in Macroeconomics for Kwasi Ameyaw

Question

The demand for good X is given by:

Qx = 200 – 0.5Px + 0.25Py –0.75Pz + 0.1M,

Research shows that the prices of related goods are given by Py = GH¢900, Pz = GH¢100, while the average income of individuals consuming this product is M = GH¢5,000.

The supply function of the company is given by: Qx = 50+ 2Px

Requirements:
a) Indicate whether goods Y and Z are substitutes or complements for good X.
b) Is X an inferior or a normal good?
c) Determine the price and quantity that will clear the market for good X.
d) Suppose an excise tax of GH¢5 per unit is imposed on the good and the company adjusts the supply function to include tax.
i. Determine the new equilibrium price and quantity in the market.
ii. Compute the deadweight loss associated with this excise tax.
e) The company has acquired a new technology which enhances its production. As result, the new supply function is Qx = 250+ 2Px. Determine the new equilibrium price and quantity in the market.

Answer 1

The demand function is:
Qx = 200 – 0.5Px + 0.25Py –0.75Pz + 0.1M = 850 - 0.5Px.
Py = GH¢900, Pz = GH¢100, M = GH¢5,000.
The supply function of the company is given by: Qx = 50 + 2Px
a) Cross-price elasticity between goods Y and Z is 0.25, so the goods are substitutes.
b) Income elasticity of demand is 0.1, so X is an inferior good.
c) The price and quantity that will clear the market for good X are:
Qd = Qs,
850 - 0.5Px = 50 + 2Px,
2.5Px = 800,
Px = 320.
Qx = 50 + 2*320 = 690 units.
d) Suppose an excise tax of GH¢5 per unit is imposed on the good and the company adjusts the supply function to include tax.
i. The new equilibrium price and quantity in the market is:
850 - 0.5Px = 50 + 2(Px - 5),
2.5Px = 810,
Px = 324.
Qx = 850 - 0.5*324 = 688 units.
ii. The deadweight loss associated with this excise tax is 5*(690 - 688) = 10.
e) The new supply function is Qx = 250+ 2Px. The new equilibrium price and quantity in the market are:
850 - 0.5Px = 250 + 2Px,
2.5Px = 600,
Px = 240,
Qx = 850 - 0.5*240 = 730 units.