Question

3) What are indifference curves and how do they relate to a budget line? Draw a graph showing 3 indifference curves and a budget line. Why is one indifference curve tangent to the budget line? What happens if the price of one good changes? (15 points). please give all three graphs.

Answer 1

An indifference curve is defined as the locus of the combinations of two goods X & Y such that the utility remains the same.

Since the consumer problem is to maximize the utility given their budget constraint. And the utility maximization requires an assumption of local non-satiation which states that if A is preferred over B then we can create a delta neighborhood around A such that a random bundle in that neighborhood will be always preferred over B. Hence utility maximization will take place on the budget line.

consumer problem: max U(X,Y)

such that Px*X + Py*Y = M

This gives the first-order condition that slope of the indifference curve(MRS) = Price ratio

Hence utility maximization occurs when the indifference curve is tangent to the budget line.

Suppose Px reduces then the budget line will shift rightward pivoted at the vertical axis because only the price of x is changed. now the initial IC will intersect at the new budget line at P & Q and hence it is not the tangent. Hence according to the local non-satiation, he will move up to the higher IC and the new equilibrium will be at B.