Question

The impact of COVID‐19 on demand can also be analysed by looking at the problem of utility maximization. Assume that a Dutch tourist derives utility from flying to the US and to Canada

(C). Her utility function equals U (US,C)= 1/2US^2/3*C^1/3 . The prices for flights are P us and P c, respectively, and the tourist’s budget for flights to the American continent is Y.

If the relative price of US and C equals 2, how many flights will the tourist buy of each type (as a function of her budget and prices)? Explain your answer, showing all appropriate derivations.

Answer 1

Utility is maximized, when MUus/MUc = Pus/Pc and all the budget is spent on these two goods.

Pus/Pc = 2.

$MUus = U'(US) = (1/2US^{2/3}*C^{1/3})' = 1/3*(C/US)^{1/3}$

$MUc = U'(C) = 1/6*(US/C)^{2/3}$

 $\frac{1/3*(C/US)^{1/3}}{1/6*(US/C)^{2/3}} = 2,$

C/US = 1 or C = US.

So, the tourist will by the same number of flights of each type.