Question

10:35 PM Mon Jan 20 42% 5 TODO of + + VIEUX UU VIL JULENT The utility of the endowment is US(6,2) = 6325; call this value Ū. The indifference curve US(B,C) = U. To find another point on this curve, pick any B and solve for C. E.g. let ! 3iC'} = 632 C = 8 so (3,8) also lies on the same indifference curve. What is Sonia's marginal rate of substitution between B and C? dCau/aB B-C C MRS = dB au/ac Bic-=-23 suppose Sonia meets up with other local candidates who are willing to trade their volunt inteers are still only willing to perform the task they signed up for, but she can trade as m unteers' time as she likes. Let the market price initially be that one hour of phone banking and one hour of canvasin be bought or sold for $10. What is Sonia's total effective budget in dollars? If she sells everything, she will have I = PBB. + PcCo = 10 x 6 + 10 x 2 = 80. Write an equation for the budget set and depict it on your graph from above. Budget set: PBB + PCC <I. Plugging in values gives 10B + 10C < 80.
Why is there a negative sign? can you please explain the derivation of this formula?

Answer 1

MRS is the amount of consumption of one good that is given up to increase consumption of another good. Since amount of one good will decrease (-) and the amount of the other good will increase (+), the sign is negative.

Mathematically,

MRS = - (MU1 / MU2), where MU: Marginal utility

Negative sign of MRS is also understood when we look at the indifference curve (IC). The IC slopes downward, so it has a negative slope as we move along the IC, reflecting the fact that as we consume more of 1 good, we consume less of the other. Since MRS is the slope of IC, the sign of MRS is negative.