Suppose goods X and Y are produced along a production possibilities frontier X² + 4Y² = 500 and they are perfect substitutes such that U = X + Y.The slope of the production possibilities frontier is .How much Y should be produced?

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Quizplus · Accepted Answer

To maximize utility (U = X + Y), we need to find the combination of X and Y that we can produce with the given resources that will give us the highest total amount of X and Y. Since X and Y are perfect substitutes, we can simply produce all Y and no X or all X and no Y.

The production possibility frontier (PPF) is given by the equation XS1U1P12S1S1P0 + 4YS1U1P12S1S1P0 = 500. We can solve this equation for Y by isolating it on one side:

4Y = 500 - XS1U1P12S1S1P0
Y = (500 - XS1U1P12S1S1P0)/4

The slope of the PPF is given as 11ea6919_dd4a_3c74_80d0_e9b18cc4c691_TB5165_11. The slope of the PPF is the amount of X we have to give up to produce one more unit of Y. Therefore, the slope is also equal to the marginal rate of substitution (MRS) between X and Y, which is the amount of X we are willing to give up to get one more unit of Y.

In this case, the MRS is simply 1, since X and Y are perfect substitutes. This means that for each unit of X we give up, we need to get one unit of Y in return to maintain the same level of utility. Therefore, we should produce Y until the marginal cost of producing Y (the amount of X we have to give up) is equal to 1.

The marginal cost of producing Y is the slope of the PPF, which is given as 11ea6919_dd4a_3c74_80d0_e9b18cc4c691_TB5165_11. Solving for Y using the equation above, we get:

Y = (500 - XS1U1P12S1S1P0)/4 = (500 - 11ea6919_dd4a_3c74_80d0_e9b18cc4c691_TB5165_11XS1S1P0)/4

Setting the marginal cost of Y equal to 1, we get:

1 = 11ea6919_dd4a_3c74_80d0_e9b18cc4c691_TB5165_11
XS1S1P0/4

Solving for XS1S1P0, we get:

XS1S1P0 = 44

Substituting this value back into the equation for Y, we get:

Y = (500 - 11ea6919_dd4a_3c74_80d0_e9b18cc4c691_TB5165_11(44))/4 = 5

Therefore, the optimal choice is to produce 5 units of Y and 0 units of X.

Suppose Goods X and Y Are Produced Along a Production