3. Indifference curves and utility: Consider the utility function U (Q1.42)241 t

Question

3. Indifference curves and utility: Consider the utility function U (Q1.42)241 that describes Robert's preferences. For the following, think of qi as the variable you would graph on the horizontal axis. Derive an expression for his marginal utility (U) from a small increase in qi holding q2 fixed. Also find the marginal utility for good 2 (U2) What is Robert's marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. Graph Robert's indifference curve for a utility level of 36. Be sure to specify at least 5 bundles of goods on the indifference curve. Does the fact that Robert's indifference curve intersects with the qi axis violate any of the 5 properties of indifference curves? Briefly support your answer. After considering the preferences represented by this utility function, provide an example of goods that might be reasonably be represented by qi and q (Hint: think about how the utility Robert derives fromm consuming good 2 differs from that of good 1 a. b. c. d. e.

Explanation / Answer

Answer for 1

d(U(q1,q2))/dq1=1+sqrt(q2/q1)

Marginal utility of good 2

d(U(q1,q2))/dq2=sqrt(q1/q2)

Answer for b)

MRS=MU(q1)/MU(q2)=(1+sqrt(q2/q1))/sqrt(q1/q2)=sqrt(q2/q1)(1+sqrt(q2/q1))

This MRS function tells q1 must be non zero and if q2<q1 then for every unit of q1 we should have to give up less than 1 unit of quantity q2

If q2>q1 then 1 unit of q1 we need to forgo more than a unit of q2.

D)

Q1 can't be zero hence it should not intersect x axis of q1

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