Answer to Question #114528 in Macroeconomics for Emmanuel

Question

a) Two students studying microeconomics are trying to understand why the tangent condition means utility is at a maximum. Let’s listen:
Student A. If a person chooses a point on his or her budget constraint that is not tangent, it is clear that he or she can manage to get a higher utility by spending differently.

Student B. I don’t get it—how do you know he or she can do better instead of worse? How can you help out Student B with a graph?

Answer 1

In Fig. 2.12, IC1, IC2 and IC3 are the three indifference curves and AB is the budget line. With the constraint of budget line, the highest indifference curve, which a consumer can reach, is IC2. The budget line is tangent to indifference curve IC2 at point ‘E’. This is the point of consumer equilibrium, where the consumer purchases OM quantity of commodity ‘X’ and ON quantity of commodity ‘Y.

All other points on the budget line to the left or right of point ‘E’ will lie on lower indifference curves and thus indicate a lower level of satisfaction. As budget line can be tangent to one and only one indifference curve, consumer maximizes his satisfaction at point E, when both the conditions of consumer’s equilibrium are satisfied:

(i) MRS = Ratio of prices or PX/PY:

At tangency point E, the absolute value of the slope of the indifference curve (MRS between X and Y) and that of the budget line (price ratio) are same. Equilibrium cannot be established at any other point as MRSXY > PX/PY at all points to the left of point E and MRSXY < PX/PY at all points to the right of point E. So, equilibrium is established at point E, when MRSXY = PX/PY.

(ii) MRS continuously falls:

The second condition is also satisfied at point E as MRS is diminishing at point E, i.e. IC2 is convex to the origin at point E.