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?
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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