Chapter 15: Problem 568

Suppose that at a given level of satisfaction the marginal rate of substitution of product \(\mathrm{B}\) for product \(\mathrm{A}\) is constant. What does this imply about the relevant indifference curve?

Short Answer

Expert verified

When the Marginal Rate of Substitution (MRS) of product B for product A is constant at a given level of satisfaction, this implies that the relevant indifference curve is a straight line that slopes downward. This represents a scenario where the consumer is willing to consistently trade the two goods B and A in a constant proportion while maintaining the same satisfaction level.

Step by step solution

Understand the concept of Marginal Rate of Substitution (MRS)

The Marginal Rate of Substitution (MRS) represents the willingness of a consumer to substitute one good for another, while maintaining the same level of satisfaction (utility). Mathematically, it is the ratio of the marginal utilities of the two goods: \[ MRS_{BA} = -\frac{MU_B}{MU_A} \] where \(MU_B\) and \(MU_A\) refer to the marginal utilities of product B and product A, respectively.

Understand the concept of an Indifference Curve

An indifference curve is a graphical representation of different combinations of two goods, A and B, that a consumer considers equally desirable, given a certain level of satisfaction. A higher indifference curve represents a higher level of satisfaction. The indifference curve is downward sloping because, as the quantity of one good increases, to maintain the same satisfaction level, the quantity of the other good must decrease.

Relationship between MRS and Indifference Curve

The MRS is the slope of the indifference curve at a particular point. If the MRS remains constant, it means that the slope of the indifference curve is constant and, therefore, the indifference curve itself is a straight line.

Conclude the properties of an Indifference Curve when MRS is constant

When the Marginal Rate of Substitution (MRS) of product B for product A is constant at a given level of satisfaction, it implies that the relevant indifference curve is a straight line that slopes downward. This represents a scenario where the consumer is willing to consistently trade the two goods B and A in a constant proportion while maintaining the same satisfaction level.

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