Bob enjoys drinking Californian and French wines and regards these two goods as perfect substitutes. Bob likes ordering wine from local wineries in California or France, so he pays in $US for Californian wines and in Euro for French wines. Suppose that a bottle of Californian wine costs $30 on average, and a bottle of French wine costs €25 on average. Since Bob is indifferent between Californian and French wines, he treats $US and Euro as perfect substitutes as well. Assume that Bob’s utility is increasing in the amount of money he can spend on purchasing wines. Let x denote the amount of $ US that Bob spends on Californian wines, and let y denote the amount of Euro that Bob spends on French wines every quarter.   (a) Write down Bob’s utility function in terms of quantities of $US and Euro: (b) Let p denote exchange rate for Euro . Let I be the income (in $USA) that Bob spends quarterly on wines. Write down Bob’s utility maximization problem and find Marshallian demand functions for each currency. (c) Let Bob allocate I = $270 per quarter to purchase wines (paying in Euro if necessary). Plot Bob’s demand function for Euro as a function of the exchange rate p. (d) Suppose, the current exchange rate for Euro is p = 1.16. What is Bob’s demand for each currency? How much wine will Bob consume? What utility level will he get?

Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
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Bob enjoys drinking Californian and French wines and regards these two goods as perfect substitutes. Bob likes ordering wine from local wineries in California or France, so he pays in $US for Californian wines and in Euro for French wines. Suppose that a bottle of Californian wine costs $30 on average, and a bottle of French wine costs €25 on average. Since Bob is indifferent between Californian and French wines, he treats $US and Euro as perfect substitutes as well. Assume that Bob’s utility is increasing in the amount of money he can spend on purchasing wines. Let x denote the amount of $ US that Bob spends on Californian wines, and let y denote the amount of Euro that Bob spends on French wines every quarter.

 

(a) Write down Bob’s utility function in terms of quantities of $US and Euro:

(b) Let p denote exchange rate for Euro . Let I be the income (in $USA) that Bob spends quarterly on wines. Write down Bob’s utility maximization problem and find Marshallian demand functions for each currency.

(c) Let Bob allocate I = $270 per quarter to purchase wines (paying in Euro if necessary). Plot Bob’s demand function for Euro as a function of the exchange rate p.

(d) Suppose, the current exchange rate for Euro is p = 1.16. What is Bob’s demand for each currency? How much wine will Bob consume? What utility level will he get?

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