A consumer chooses an optimal consumption point where the a. slope of the indifference curve exceeds the slope of the budget constraint by the greatest amount. b. ratio of the marginal utilities equals the ratio of the prices. c. marginal rate of substitution is maximized. d. all of the above are correct.
The Correct Answer and Explanation is:
ChatGPT said:
Correct Answer: b. ratio of the marginal utilities equals the ratio of the prices.
In consumer theory, the optimal consumption point occurs where a consumer maximizes utility subject to a budget constraint. This point is found where the consumer’s indifference curve is tangent to the budget line. At this point, the marginal rate of substitution (MRS) between the two goods is equal to the ratio of the prices of the two goods.
Mathematically, this condition is expressed as:MUxMUy=PxPy\frac{MU_x}{MU_y} = \frac{P_x}{P_y}MUyMUx=PyPx
Where:
- MUxMU_xMUx and MUyMU_yMUy are the marginal utilities of goods xxx and yyy respectively
- PxP_xPx and PyP_yPy are the prices of goods xxx and yyy respectively
This equation ensures that the consumer is receiving the same utility per dollar spent on each good. If this condition is not met, the consumer can increase total utility by reallocating spending from one good to another.
Let’s analyze the incorrect options:
- a. The slope of the indifference curve (which is the MRS) should not exceed the slope of the budget constraint. At optimal consumption, they are equal, not maximized or different.
- c. The MRS is not maximized at the optimal point. In fact, it is simply equal to the price ratio, reflecting a point of tangency, not a maximum.
- d. “All of the above” is incorrect because only option (b) is accurate. Options (a) and (c) misstate how consumer optimization works.
Therefore, option (b) is correct because it accurately represents the key condition for utility maximization given a consumer’s budget. This point reflects economic efficiency in consumption, where no further gains in utility can be achieved by reallocating resources
