chapt 86 REVEALED PREFERENCE (Ch.7 7.5 (0) Horst and Nigel live in different cou

Question

chapt 86 REVEALED PREFERENCE (Ch.7 7.5 (0) Horst and Nigel live in different countries. Possibly they hav consume only two goods, r and y. Horst has to pay 14 marks per unit o different preferences, and certainly they face different prices. They eac r and 5 marks per unit of y. Horst spends his entire income of 167 marks on 8 units of and 11 units of y. Good x costs Nigel 9 quid per unit and good y costs him 7 quid per unit. Nigel buys 10 units of r and 9 units of y. (a) Which prices and income would Horst prefer, Nigel's income and prices or his own, or is there too little information to tell? Explain your answer. Horst prefers Nigel's budget to his own. With Nigel's budget, he can afford his own bundle with money left over (b) Would Nigel prefer to have Horst's income and prices or his own, or is thore too little information to tell? There is too little information to tell

Explanation / Answer

b) Since Horst's budget set is not a proper subset of Nigel's and we don't know Nigel's preferences, so there is a possibility that Nigel might like some bundle in Horst's budget set (that he can't afford in his current budget) more than the bundle of his choice from his own budget set. So, we can't tell.
For example:
Given the data: Horst chose (8, 11) from the budget 14x + 5y = 167

And Nigel chose (10, 9) from 9x +7y = 153
If Nigel's utility function is u(x, y) = 9x + 7y then he will prefer Horst's budget to his own.
And If Nigel's utility function is u(x, y) = min{9x, 10y} then he will prefer his own budget to Horst's

So we cannot say that Nigel would prefer to have Horst's income and prices or his own.

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