Question

For questions 8-10 assume that Katy has preferences for sleeping and partying which can be described by the utility function ? = ? 2? 2 with marginal utilities ??? = 2??2 , ??? = 2? ?2 .

8. Given Katy’s utility function, the corresponding indifference curves slope upward/downward and become flatter/steeper (a) upward, flatter (b) upward, steeper (c) downward, flatter (d) downward, steeper

9. Given Katy’s utility function, she needs to give up increasing amounts of sleeping hours in order to visit one more party and remain as well off. (a) True (b) False

10. According to the MRS, what’s the maximum number of sleeping hours Katy would be willing to give up to visit one more party, if she currently visits 2 parties and sleep 8 hours per day? (a) 1 4 (b) 1 2 (c) 2 (d) 4

Answer 1

8).

Here Katy’s utility function is “U = S²*P²”, the slope of the indifference curve is given by.

=> dS/dP = (-1)* MU_P/ MU_S = (-1)*(2PS²)/(2SP²) = (-S/P) < 0, => the IC is downward sloping from right to left.

=> d²S/dP² = (-1)*[P*(dS/dP) – S]/P² = (-1/P²)*[P*(-S/P) – S] = (-1/P²)*(- 2*S) = (2*S/P²) > 0, => the indifference curve is convex, => it is getting flatter. The correct answer is “C”.

9).

Here the 2^nd order differentiation is positive, => she needs to give up increasing amounts of sleeping hours in order to visit one more party and remain as well off, => the statement is TRUE.

10).

The MRS is given by, => MRS = S/P = 8/2 = 4, => she is willing to give up “4 hours” to visit one more party.