Question

2) (5pts.) Consider a consumer whose preference satisfies all the assumptions we stated in class (com- pleteness, transitivity, monotonicity, and decreasing marginal rate of substitution) and also has smooth indifference curves. If we know that the consumer prefers the bundle (1,5) to the bundle (2,1) what can we say about the marginal rate of substitution of good 2 for good 1 at the bundle (1,5) (state if the marginal rate of substitution is greater, less, or equal to some number). Explain your reasoning.

Answer 1

It is given that the consumer prefers bundle (1,5) to (2,1). The Marginal Rate of Substitution (MRS) between two bundles of goods tells how many units of Good X must be given up in order to gain one additional unit of Good Y so that the consumer remains on the same utility curve. The MRS can be calculated using the formula; dx/dy. Here dx signifies the change in the amount of Good X whereas dy signifies the change in the amount of good Y.

The MRS between the two bundles given in the question is as follows:

we can say that if quantity of X falls by 1, i.e. 1-2 = -1, then for consumer to attain the same level of utility, the quantity of Y should increase by 4, i.e. 5-1.

MRS is the absolute value of dx/dy =1 /4 .

The value of MRS at (1,5) will be lesser than 1 /4 because the point (1,5) is preferred more by the consumer than the point (2,1). Hence, the consumer is getting more utility at point (1,5) and will want more units of Good Y for each unit of Good X given up when he is at (1,5) because he will value Good X more at the point (1,5).