Question

Suppose demand for dodge chargers was estimated to be represented by

Qdc = 300 - 3.0Pc - 10,000Pg + 1.75M + .2A

Where Pc is price of Dodge Chargers, Pg is price of gasoline, M is consumer income and A is cost of advertising.

A. If Dodge was selling 150,000 Chargers at $30,000, what is the own-price elasticity of demand?

     How much would quantity demand change if price was reduced to $26,000? What would happen to revenue?

B. If Dodge was selling 150,000 Chargers when average consumer income was $60,000, what is the income elasticity?

     What would happen to quantity demanded if the average consumer income fell to $54,000?

C. If Dodge was selling 150,000 Chargers when the price of gasoline was $2.25, what is cross-price elasticity?

     If the price of gasoline rises 10%, how much would the number of Chargers sold increase or decrease?

Answer 1

A) Own Price Elasticity of demand = (∆Qc / ∆Pc) * (Pc / Qc)                 [Where, ∆Qc/∆Pc is the price coefficient in the demand function]

                                                        = -3.0 * (30,000 / 150,000)

                                                        = -0.6

The absolute value of PED is 0.6.

If price was reduced to $26,000 from $30,000, quantity demanded will increase by 12,000 (i.e.3.0 *4000)

Since the absolute value of PED is less than 1, it means demand for charger is inelastic. So, a decrease in price will lead to decrease in revenue.

B) Income Elasticity of demand = (∆Qc / ∆M) * (M / Qc)            [Where, ∆Qc/∆M is the income coefficient in the demand function]

                                                  = 1.75 * (60,000 / 150,000)

                                                  = 0.7

If income falls to $54,000 from $60,000, quantity demanded will decrease by 10,500 (i.e.1.75 *6000).

C) Cross-Price Elasticity of demand = (∆Qc / ∆Pg) * (Pg / Qc)                      [Where, ∆Qc/∆Pg is the gasoline price coefficient in the demand function]

                                                  = -10,000 * (2.25 / 150,000)

                                                  = -0.15

Since, CPED is negative, it means charger and gasoline are complementary goods.

An increase in price of gasoline will lead to a decrease in quantity demanded of chargers

If the price of gasoline rises 10%, the new price of gasoline = 2.25 *1.10 = $2.475

Decrease in charger sold = 10,000 * (2.475 - 2.25) = 2,250