Question

A wealthy consumer's preferences are strictly convex and his demand for good X (disinfectant wipes) is independent of his income and given by

X = 60.9 - 3.7 P_{x}/P_{y}

where P_{x} and P_{y} are respectively the price
of good X and the price of good Y.

Suppose prices are such that the consumer buys 5 units of good X in order to maximize his utility. What is the consumer's marginal rate of substitution (of good X in terms of good Y) equal to?

Answer #1

The Marginal Rate of Substitution is defined as the amount of one good the consumer is willing to give up to get one additional unit of another good and maintain the same level of satisfaction.

In this case, consumer's preferences are strictly convex which implies the MRS is equal to the price ratio.

MRS_{XY} = Price of X / Price of Y

that is, the slope of the indifference curve is equal to the slope of the budget line.

Given X = 60.9 - 3.7 P_{x} / P_{y}

5 = 60.9 - 3.7 P_{x} / P_{y}

P_{x} / P_{y} = 60.9 - 5 / 3.7 = 55.9 / 3.7 =
56/4 = 14

As, MRS_{XY} = Price of X / Price of Y

therefore, Consumer's MRS_{XY} = 14:1

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(d) Are there any similarities or diﬀerences between the two
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