Question

In: Economics

Let U=X1/2Y2, dU/dX=(1/2)X-1/2Y2, dU/dY=2X1/2Y Px=$15, Py=$3 and I=$300 For the rest of this problem, suppose Px...

Let U=X1/2Y2, dU/dX=(1/2)X-1/2Y2, dU/dY=2X1/2Y Px=$15, Py=$3 and I=$300

For the rest of this problem, suppose Px has decreased to $6.

11.(2 pts) _________________________What is the value of Y on the new income consumption curve when X=6?

12. (5 pts) _______________________________________ Find the new values of X, Y and U which maximize happiness.

13.(4 pts)________________________________________What is the equation for the PCC for X (X as a function of Y or Y as a function of X) for Py=$3 and I=$300?

Expert Solution

The value given in the question are as follows:

Now, the question assumes that the price for good x has fallen and the new price is $6, that is

11. Since the utility given to us is, that is the utility the consumer gaines from consuming both the goods is in the ratio of 1:2. Thus the consumer is wiling to spend more on Good Y than Good X. And an income consumption curve, in general is defined as the curved that plots the two goods on the two axis and there after analysis the spending on the goods with respect to the given budget lines. The locus of all the points on different given budget lines frame out the income consumption curve.
Where budget line is the ratio between the prices of both the goods, that is .

In the given question, the original budget line is, .

And the new budget line is, .

Thus it is clear that the ratio of the prices of both goods has fallen, causing an inward shift of the budget line.

The value of Y for X given 6 can be calculated as, i.e. or .

In the given question the price for good x has fallen thus, the consumption for good X will increase as per the law of demand. Supporting the Argument numerically, and .

Thus the consumer moves to a higher IC on the budget line.

Therefore, The value of Y given X=6, will be 12. As the ratio od optimal utility is given to be 1:2 that is if the bundle has 1 unit of good X than it will have 2 units of good Y.

Rahul Sunny answered 1 year ago

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