Question

Is consumer equilibrium possible under the condition of convexity?

Answer 1

1. Convex Indifference Curves Reflect Diminishing MRS: When a consumer switches from one good to another, the Marginal Rate of Substitution (MRS) between the two goods decreases, according to a convex indifference curve. A balanced trade-off requires this declining MRS, which enables the consumer to get to a point where the rate at which they are willing to substitute is equal to the market price ratio.
2. Tangency Condition for Equilibrium: When the budget line is tangent to the maximum indifference curve, consumer equilibrium is reached. Only convex curves provide this tangency since they permit a single point of tangency that represents the ideal pairing of two products.
3. Stability of Equilibrium: A change from the equilibrium point lowers overall satisfaction with convex curves, making the equilibrium stable and desirable. The customer could always move to a better spot if the curve were concave, which would indicate that no actual equilibrium is achieved.