Question

2. Supply, Demand and Elasticity: The demand for a product is Qd=200-5P-2Px and supply is Qs=10+2P, where Q is the quantity of the product, in thousands of units, P is the price of the product, and Px is the price of another good X.

A. When Px = $25, what is the equilibrium price and quantity sold of the product?

B. At the equilibrium price and quantity, what is the own price elasticity of demand for the product?

C. What is the cross-price elasticity of demand for the product at the equilibrium price and quantity?

D. Does the cross-price elasticity provide enough information to determine whether the product and good X are complements or substitutes? If Yes, are they complements or substitutes? If No, why not?

Answer 1

2(A)

When P_X = 25, then demand function became

Q_d = 200 - 5P - (2 * 25)

Q_d = 150 - 5P

Now to determine the equilibrium price and quantity, we need to equate Q_d and Q_s.

150 - 5P = 10 + 2P

7P = 140

P = 20.

Now, if we put P = 20 in either on demand equation or supply equation we will get equilibrium quantity.

Q_d = 150 - 5P

Q_d = 150 - (5 * 20) = 50

So, the equilibrium price and quantity sold of the product is $20 and 50 units respectively.

2(B)

Now, to calculate the own price elasticity we need to use the following formula

e = (dQ_d / dP) * (P / Q_d )

Given the demand function, Q_d = 150 - 5P

dQ_d / dP = - 5

So, at equilibrium price and quantity, the own price elasticity of demand is

e = (- 5) * (20 / 50)

e = - 2.

So, at the equilibrium price and quantity, the own price elasticity of demand for the product is - 2.

2(C)

Now, to calculate the cross-price elasticity we need to use the following formula

e = (dQ_d / dP_X ) * (P_X / Q_d )

At equilibrium price P = 20, the demand function, Q_d = 200 - (5 * 20) - 2P_X = 100 - 2P_X

dQ_d / dP_X = - 2

So, at equilibrium price and quantity, the own price elasticity of demand is

e = (- 2) * (25 / 50)

e = - 1.

So, at the equilibrium price and quantity, the cross-price elasticity of demand for the product is - 1.

2(D)

From theory, we knew that complementary goods have negative cross-price elasticity and substitute goods have positive cross-price elasticity.

So, in this case, cross-price elasticity is - 1. That means negative.

So we can say that, the product and good X are complements.