Question

2. Suppose you can describe your preferences by the utility
function U =
2q_{S}^{0.8}q_{M}^{0.2}.

(a) Which good, ski lift tickets or meals out, provides you with greater marginal utility when you have equal quantities of each?

(b) Provide a formula for the slope of any indifference curve (the Marginal Rate of Substitution) between ski lift tickets and meals out.

(c) What happens to your Marginal Rate of Substitution as the number of ski lift tickets you purchase increases (i.e., does the absolute value of the MRS increase, decrease, or remain the same)? Give a brief intuitive explanation why this makes sense.

Answer #1

The utility function isU = 2qS^0.8 qM^0.2.

(a) Find the marginal utility of both goods

MUqS = 2*0.8*(qM/qS)^0.2 and MUqM = 2*0.2*(qS/qM)^0.8

When qS = qM, MUqS is 1.6 and MUqM is 0.4. Hence ski lift tickets provides you with greater marginal utility when you have equal quantities of each

(b) MRS = - MUqS/MUqM

= -1.6*(qM/qS)^0.2 / 0.4*(qS/qM)^0.8

= -4qM/qS

This is the value of MRS

(c) As the number of ski lift tickets you purchase increases the MRS will fall down because to have more of some goods we need to have less of other goods. Also MRS is a falling value along the convex shaped indifference curves.

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