Given the following utility function: U = 10X + 2Y and marginal utilities: MU_x = 10, MU_y = 2 A consumer facing the following prices: P_x = $1, P_y =2 chooses to consume: 11 units of good X and 16 units of good Y. Assume that graphically good X is on the horizontal axis and good Y is on the vertical axis. Given this consumption bundle, the marginal rate of substitution is equal to - (Note that the minus sign is already included.).

5

Explanation:

In economics, the marginal rate of substitution (MRS) refers to the unit of good X that a consumer is ready to give up in order to consume an additional unit of good Y in order to maintain the same level of satisfaction.

Since it is assumed graphically that good X is on the horizontal axis and good Y is on the vertical axis, the MRS of good X for good Y is given as follows:

MRSx,y = - (dy/dx) = MU_x/MU_y (1)

Where,

MRSx,y = marginal rate of substitution of X for Y = ?

Marginal utility of X = MU_x = 10

Marginal utility of Y = MU_y = 2

Substituting the values into equation (1), we have:

MRSx,y = 10/2 = 5

Note that since the minus sign is already included, this gives us -5 and it is interpreted that the consumer is ready to give up 5 units of Y to have an extra unit of X.

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