Roger's utility function is U = min{a 1 , a 2 } min{b 1 , b 2 }, where a 1 and a 2 are the number of piano lessons he consumes this year and next and b 1 and b 2 are the number of ice skating lessons he consumes this year and next.The price of piano lessons is $10 each and the price of ice skating lessons is $4 each.The prices won't change, but the interest rate is 7%.If Roger consumes 20 piano lessons this year, how many ice-skating lessons will he consume next year?A) 50B) 20C) 40D) 30E) There is not enough information to be able to tell.

Question

Roger's utility function is U = min{a 1 , a 2 } min{b 1 , b 2 }, where a 1  and a 2  are the number of piano lessons he consumes this year and next and b 1  and b 2  are the number of ice skating lessons he consumes this year and next.The price of piano lessons is $10 each and the price of ice skating lessons is $4 each.The prices won't change, but the interest rate is 7%.If Roger consumes 20 piano lessons this year, how many ice-skating lessons will he consume next year?A) 50B) 20C) 40D) 30E) There is not enough information to be able to tell.

Mieann Pondoy · Accepted Answer

Final Answer : A, Explanation :  The marginal rate of substitution between piano lessons and ice skating lessons is equal to the ratio of their prices, which is 10/4 = 2.5. This means that Roger is willing to give up 2.5 ice skating lessons for each additional piano lesson.Since Roger consumes 20 piano lessons this year, he is willing to give up 20 * 2.5 = 50 ice skating lessons. Therefore, he will consume 50 ice skating lessons next year.

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