A household must decide between consuming good 1, C1, and consuming good 2, C2. The budget constraint for this household is: P1*C1 + P2*C2 = Y, and the utility function is: u(C1) + u(C2). The slope of the indifference curve is always equal to:

Question

BlackTom AI · Accepted Answer

When analyzing the slope of an indifference curve for a consumer with a utility function u(C1) + u(C2), the key concept is the marginal rate of substitution (MRS) between the two goods. The MRS tells us how much of good 2 the consumer is willing to give up to gain an additional unit of good 1, while remaining on the same level of utility.

Option 1: 'The ratio of consumption of good 1 to the consumption of good 2.' This is not the slope of the indifference curve. The ratio C1/C2 describes a particular point on the curve, not its slope. The slope is about marginal trade-offs, not a simple ratio of quantities.

Option 2: 'The ratio of the price of good 1 to the price of good 2.' This ratio reflects the budget constraint, specifically the slope of the budget line (-P1/P2) in a standard two-good model, not the slope of the indifference curve. It does not represent the consumer’s marginal willingness to substitute between goods.

Option 3: 'The ratio of goods prices to income.' This statement conflates budget composition with indifference-curve slope; while prices and income shape feasible choices, they do not determine the slope of the indifference curve itself, which is driven by marginal utilities.

Option 4: 'The marginal rate of substitution between good 1 and good 2.' This is the correct description of the slope of the indifference curve. The slope equals MU1/MU2, i.e., the rate at which the consumer is willing to trade good 2 for an extra unit of good 1 while keeping utility constant.

Across these options, the only description that matches the concept of the indifference-curve slope is the marginal rate of substitution between the two goods.

A household must decide between consuming good 1, C1, and consuming good 2, C2. The budget constraint for this household is: P1C1 + P2C2 = Y, and the utility function is: u(C1) + u(C2). The slope of the indifference curve is always equal to: 单项选择题

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A household must decide between consuming good 1, C1, and consuming good 2, C2. The budget constraint for this household is: P1*C1 + P2*C2 = Y, and the utility function is: u(C1) + u(C2). The slope of the indifference curve is always equal to: 单项选择题