Suppose you work for an investment firm in New York City. You derive utility fro

Question

Suppose you work for an investment firm in New York City. You derive utility from consumption, as described by the utility function U(C). where C denotes consumption and U(middot) is an increasing function. Consumption is a composite of food and housing given by C = squarerootC_F squarerootC_H. where C_F and C_H denote, respectively, consumption of food and housing. Suppose that in your current job. you make dollar 250,000 per year. Your company offers you a one-year position in its Bolivian branch located in La Paz. Your boss would like to know what would be the minimum income (in dollars) you would require to be willing to work in La Paz. In NYC the price of food is dollar50 per unit and and the price of housing is dollar750 per unit. Food is internationally traded, but housing is nontradable. 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). The answer to this question is just one number, i.e., the minimum income you require to be willing to work for one year in La Paz. but you have to show your work and provide intuition. How many units of food and housing do you consume in NYC and how many would you consume in La Paz with your minimum required income? Provide intuition.

Explanation / Answer

The minimum income would the one where i get the same utlity by staying in La Pas as i get in NYC.So my comsumption of Food and Housing shoud be same in the two places.

So In NYC, C = (CF)^1/2*(CH)^1/2

MUH = dC/dCH = 1/2*(CF/CH)^1/2

MUF = dC/dCF = 1/2*(CH/CF)^1/2

So, Putting the utility maximization condition in new york

MUF/MUH = PF/PH

[1/2*(CH/CF)^1/2]/[ 1/2*(CF/CH)^1/2] = 50/750

CH/CF = 1/15

and budget constraint in NYC

50CF + 750CH = 2,50,000

50*15CH + 750*CH = 2,50,000

CH = 2,50,000/1500

CH = 166.66

s0 CF = 15*CH = 15*166.66 =2499.9

So , to have same consumption of house in La pas = 166.66*2000 = 3,33,320

Price of food in Las = exchange rate*P = 5*50 = 250 pesos

So , to have same consumption of food in La pas = 2499.9*250 = 6,25,000

So total Income should be = 333,320 + 6,25,000 = 9,58,320pesos

= 958308.33 /50 = 191664 Dollars

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