Suppose you work for an investment firm in NYC. You derive utility...

Suppose you work for an investment firm in NYC. You derive utility from consumption, as described by the utility function U(C), where C denotes consumption and U(·) is an increasing function. Consumption is a composite of food and housing given by

C = sqrt(Cf)sqrt(CH) ,

where CF and CH denote, respectively, consumption of food and housing. Suppose that in your current job, you make $250,000 per year. Your company offers you a one-year position in its Bolivian branch located in La Paz. In NYC the price of food is $50 per unit and the price of housing is $750 per unit. Food is internationally traded, but housing is non-tradable. The dollar/Bolivian peso exchange rate is 5 pesos per dollar. The price of housing in La Paz is 2,000 pesos. Suppose that all you care about is to maximize your utility and that you always spend all of your income in consumption (no savings).

(a) What is the price of the composite consumption good in NYC?

(b) What is the price of the composite consumption good in La Paz?

(c) What income in dollars would allow you to buy the same number of composite consumption goods in La Paz as in NYC, i.e. C = C ∗ ? 1

(d) What income in pesos would allow you to have the same utility in La Paz as in NYC?