Question

Jerry Seinfeld derives utility from only two goods: Puffy shirts (X) and cereal (Y). His utility function is: U = XY'. The price of X is $10, the price of Y is $20, and Jerry has an income of $500. Suppose the price of Puffy Shirts increased to $20. The compensated bundle is (2.6794, 24.1149). How much is the total effect, on X, of the price change?

Answer 1

The total effect of change in the price of goods X is that the consumption of goods X is decreased from 2.5 by find out the new utility line.

What is Utility?

Utility is the very important term that is used in the economics. It refers to the want satisfying power of any commodity, that satisfy the wants of each and every individual.

According to the given information,

$U = XY^9$

Old Budget Line:

$500 = 10X +20Y$

We know that,

$\frac{MUx}{Px} = \frac{MUy}{Py}$

Now, find the value of $MU_x$ and  $MU_y$,

$MU_x = \dfrac{\triangle U}{\triangle x}\\\\MU_x = Y^9$

$MU_y = \dfrac{\triangle U}{\triangle y}\\\\MU_y = 9 \times XY^8\\\\MU_y = \dfrac{Y^9}{10} \times \dfrac{9 \times XY^8}{20} \\\\Y = \dfrac{9X}{2}$

Now, put the value of Y in the above budget line, we have,

$\ 500 = 10X+20Y\\\\\ 500 = 10X + 20(\frac{9X}{2} )$

Then, the value of X would be,

$X = 5$

Now, put the value of X in Y,

$Y = \dfrac{9X}{2}\\\\Y =\dfrac{9\times 5}{2}\\\\Y = 22.5$

Then, the new budget line would be:

$500 = 20X +20Y$

We know that,

$\frac{MUx}{Px} = \frac{MUy}{Py}$

No, put the value of $Y = 9X$ in the new budget line, we get

$500 = 20X +20(9X)$

Then, the value of X is:

$X = 2.5$

Then the value of Y is:

$Y = 9X\\Y =9\times 2.5\\Y= 22.5$

Therefore, the effect of the change in the price of X is that the consumption of X had fallen from 5 to 2.5. Then the effect of price change on the consumption of good X is -2.5.

Learn more about utility, refer to:

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