Question

1. When a consumer maximizes utility, which of the following is NOT true? a. The indifference curve is tangent to the budget line b. Marginal utility per dollar is maximized c. The marginal rate of substitution is equal to the relative price d. The marginal utility per dollar spent is equal across all goods

Answer 1

Answer 1

The correct answer is (b) Marginal Utility per dollar is maximized.

In order to maximize utility a consumer consumes at a point where Budget line is tangent to the indifference curve. Hence statement (a) is correct.

Slope of budget line is Ratio of prices(or relative prices), Slope of Indifference curve is Marginal Rate of substitution.

Hence Utility maximizing condition is Budget line is tangent to the indifference curve this means that slope of budget line and Indifference curve is equal i.e. MRS = relative prices.

Hence statement (c) is also true

Lets see for a 2 good case and let that good be A and B.

MRS = MU_A/MU_B and Slope of Budget line = P_A/P_B

where MU_X means marginal utility of X and P_X means price of good X.

Utility maximizing condition MRS = relative prices => MU_A/MU_B = P_A/P_B

=> MU_A/P_A = MU_B/P_B

hence marginal utility per dollar should be equal for all goods. Similarly is for n good case. Hence Utility will be maximized when Marginal utility per dollar will be equal for all goods and not when Marginal Utility per dollar is maximized. Hence statement (d) is correct and statement (b) is Not True.

Hence, the correct answer is (b) Marginal Utility per dollar is maximized.