Question

1.     Suppose a consumer has an income of $100. P1=10 and p2=10.

a. Draw the consumer’s budget constraint

b. On the same drawing, add an indifference curve on which the optimal basket lies. Assume the indifference curve is convex as usual

c. On the same drawing, add an indifference curve which has a lower utility level than the optimal basket. Make sure to include the intersections of the curve with the budget constraint, and carefully explain why they cannot be optimal although they are on the budget line.

Answer 1

a)

b & c)

The consumer's problem is to maximize the utility subject to the budget constraint. this will be achieved when the budget line will be tangent to the IC. Optimum can't be interior-point because of the assumption of local non-satiation.

Another IC1 below the IC0 implies lesser utility as more is better. Hence the point like P &Q where the IC intersects the budget line will not be the optimum because given the same budget line a consumer can attain a high utility level at IC0.

Also mathematically, we know that the MRS = P1/P2

=> MUx1/MUx2 = P1/P2

=> MUx1/P1 = MUx2/P2

which is nothing but the slope of the budget line should be equal to that of the IC.

Hence the optimum level output is only at point Q.