For Questions 24 to 30, please consider a consumer that purchases Good X and Goo

Question

For Questions 24 to 30, please consider a consumer that purchases Good X and Good Y. Good X is an inferior good and Good Y is a normal good. The price of Good X is $25 per unit. The price of Good Y is $10 per unit. Initial income is $400.

Given this info, # of x, = 16 on the budget constraint which I understand because 400/25=16, but # of Y is supposively 25 and not 400/10=40. Why is this the case?

25. What is the slope of the indifference curve at the optimum point for this consumer with this budget constraint? a) -2.5 b) - 2 c) - 1 d) - 1/2 e) Not Given

The answer is A, but how do I find it given info from the first part? Please explain step by step. Thank you

Explanation / Answer

Slope of indifference cure = Marginal utility of good X/Marginal utility of good Y this is equal to MRS i.e. marginal rate of substitution.

At optimum level MRS = -Px/Py

So Slope of indifference curve at optimum point = -Px/Py = -25/10 = -2.5

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