Question

2. Suppose household annual demand for gasoline follows the equationQD = 2000 – 500P + 25I where P is the price of a gallon of gasoline and I is household income in 1000s of dollars.Suppose that P = 3 and I = 60.What quantity of gasoline will households demand at this price and income level?__________What is the income elasticity of demand for gasoline at this price, income, and quantity level?__________What happens to the income elasticity of gasoline demand if I rises from 60 to 100?It _____________ (rises/falls) to ______________.Does this change in elasticity make gasoline buying more or less sensitive to income changes?

Answer 1

Q_D = 2000-500P+25I (where P=$3, I=$60,000)

or, Q_D = 2000-(500*3)+(25*60,000)

or, Q_D = 2000 - 1500 + 1,500,000

or, Q_D = 1,500,500

Now, dQ_D/dI = 25

Then, Income elasticity of demand = Change in quantity demanded / Change in income = dQ_D/Q_D / dI/I = I/Q_D * dQ_D/dI = 60,000/1,500,500 * 25 = 0.99 = 1 (approx)

If I increases from $60,000 to $100,000

Q_D = 2000 - (500*3) + (25*100,000)

or, Q_D = 2,500,500

Again, dQ_D/dI = 25

Then, new income elasticity of demand = Change in quantity demanded / Change in income = dQ_D/Q_D / dI/I = I/Q_D * dQ_D/dI = 100,000/2,500,500 * 25 = 0.99 = 1 (approx)

Thus, we can see that income elasticity neither rises nor falls.

Here, we can say, that income elasticity of demand for gasoline is insensitive to changes in income.