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John consumes two goods, X and Y. The total utility function is as follows: The price of X is $9, and the price of Y is $12. a. Write an expression for John's MRS. b. What is the optimal mix between X and Y in John's market basket

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Johns MRS (Marginal Rate of Substitution) is given as: | MRS[tex]_{xy}[/tex]  |  = dy/dx = MUy/MUx'.



What is Marginal Rate of Substitution?

The marginal rate of substitution (MRS) is an economic indices that evaluates the units of good X that John is willing to give up for another unit of good Y. The assumption here, is that both goods provide John with the same amount of utility.

What is the expression for John's MRS?

The expression of John's MRS is given below:

Johns MRS Expression is given as:

| MRS[tex]_{xy}[/tex]  |  = dy/dx = MUy/MUx'

Where X and Y refers to the two goods that John consumes

d'y/d'x = derivates of y as regards x

MU = Marginal utility of two goods, that is goods Y and goods X.

What is the Optimal Mix of X and Y?

MRS = Px/Py
Y/X = 9/12

= 0.75

It is therefore recommended that John consume 0.75 Ys in relation to X.

Learn more about Marginal Rate of Substitution at;
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