Hi, I working on a problem for my Intermediate Micro Theory classand I\'m stuck

Question

Hi, I working on a problem for my Intermediate Micro Theory classand I'm stuck on a problem. The problem is : Suppose you consume 3apples per week, and your marginal utility for apples is 10; andyou consume 5 bananas per week, and your marginal utility forbananas is 20. What must be true about the prices of apples andbananas, so that your choice is optimal?

I know that marginal utility of x is the partial derivative ofutility divided by the partial derivative of x and the same foryou. But, the problem is that I don't know how to apply that to theproblem. Any advice or help would be greatly appreciated. Thankyou.

Explanation / Answer

Im thinking that the marginal utility to price ratio must be equalfor the each good. a = apple b = banana MRS = Ua/Pa = Ub/Pb Ua/Ub = Pa/Pb 10/20 = Pa/Pb = So you get the price ratio

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