Supply and Demand and Marginal Cost

1i) Demand function for air travel between the U.S. and Europe has been estimated to be: ln Q = 2.737 - 1.247 ln P +1.905 ln I where Q denotes number of passengers (in thousands) per year, P the (average) ticket price and I the U.S. national income. Determine the price elasticity and income elasticity of demand (8 points).
From Lecture Module 3 Equation 4 we learned the alternative formulation of elasticity.
Alternative formulation of elasticity
EP = dQ/dP * P/Q = dlnQ/dlnP Natural log: ln, uses the base “e” How? ∂lnQ/∂lnP =(d lnQ/dQ) * (dQ/dP) * (dP/dlnP) [ Note: dY/dX = 1/(dX/dY) since, dlnX/dX = 1/X, dX/dlnX = X]

Example: Q = AP-α A:Constant>0 lnQ=lnA + ln(P-α) =lnA – αlnP EP = dlnQ/dlnP = -α

∝ =∆lnQ/∆lnP
∝ =P/Q* (∆Q/∆K) = Elasticity
The coefficients of double log model are the corresponding elasticity
Price elasticity = -1.247
Income elasticity = 1.905

(1ii) It has been estimated that the price elasticity of demand for U.S. manufactured automobiles is -1.2, while the income elasticity of demand is 2.0 and the cross price elasticity of demand with respect to the foreign automobiles is 1.5. The current volume of sales for U. S. manufactured automobiles is 10 million per year. It is expected that over the next year the average income of the consumers in the U.S. will increase by 2.5 percent. It has been determined that the price of the foreign imports will increase by 6% over the next year. By how much should the U.S. automakers adjust the price of their automobiles if they wish to increase the volume of their sales by 9.2% next year (8 points)?
Price elasticity = -1.2
Income elasticity = 2
Cross price elasticity = 1.5
Current volume = 10 million
2.5% Average income increase
We know from Module 3 created by Dr. Ghosh that:
EP = %ΔQx / %ΔPx, where only Px changes
%ΔQx = EP * %ΔPx if only Px changes
Exy = %ΔQx / %ΔPy, where only Py changes
%ΔQx = Exy * %ΔPy, if only Py changes
EI = %ΔQx / %ΔI,