PROBLEM #3 An econometrician has determined that the regional demand for new mid
ID: 1248796 • Letter: P
Question
PROBLEM #3
An econometrician has determined that the regional demand for new mid-sized cars is represented by the following equation:
Qd=27,150-.5P+.02Pt-2,400Pg+2Y
In this equation, P is the price of mid-sized cars, Pt is the price per trip on public
transport, Pg is the price per gallon of retail gasoline, and Y is the average hourly income in the region. Suppose that the current price per trip on public transport is $2, the price per gallon of gasoline is $3, and the average hourly income is $25 for this region. In addition, assume that today’s market-equilibrium price for a mid-sized car is $30,000. Find the market equilibrium quantity of mid-sized cars. Next, calculate the following: price elasticity of demand for mid-sized cars; income elasticity of demand for mid-sized cars; cross-elasticity of demand relative to public transport; and cross-elasticity of demand relative to gasoline. Given your results for the last two elasticity measures, comment on the degree of substitutability or complementarity between public transport and gasoline relative, respectively, and cars.
Explanation / Answer
Qd=27150-.5P+.02Pt-2400Pg+2Y Qd=27150-.5*30000+.02*2-2400*3+2*25 Q=5000 Price Elasticity = s(P/Q), where s is slope with respect to price. Price Elasticity= .5(30000/5000)=3 Income Elasticity= s(I/Q), where s is slope with respect to income. Income Elasticity=2(25/5000)=0.01 Cross-Price Elasticity with Public = s(Pt/Q), where s is the slope with respect to the price of public and Pt is the price of public transit. Cross-Price Elasticity with Public =-.02(2/5000)=-0.000008 Cross-Price Elasticity with gas= s(Pg/Q), where s is the slope with respect to the price of gas and Pg is the price of gas. Cross-Price Elasticity with gas=2400(3/5000)=1.44 Cars are normal goods. They are weak substitutes to public transit and strong compliments with gasoline.
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