Suppose that the utility function of a consumer is U(x,y) = x ¼y ¾, where x...

Suppose that the utility function of a consumer is U(x,y) = x ^¼y ^¾, where x and y are the quantities of the good X and good Y consumed, respectively. The consumer's income is 400.

(a) What is the demanded bundle when the price of good X is 10 and the price of good Y is 10?

(b) Redo part (a) when the price of good X is doubled?

(c) Redo part (a) when the price of good Y is doubled (the price of good X is still 10)?

Expert Solution

a)

The given function is a Cobb-Douglas Utility function of the form where a is 1/4 and 1-a is 3/4. The demand for any Cobb-Douglas utility function is given by

The demand shows that the amount of each good consumed is equal to the fraction of income spent on it (a for x and 1-a for y) divided by the price of the good.

b) Here, the price of x is doubled by that of y is the same

Here, the quantity of x consumed changes but that of y remains the same because the income allocated to each good remains the same. Since the price of x has changed, less of it can be consumed. And as the price of y hasn't changed, same quantities of y can be consumed.

c) Now the price of y has doubled.

The same explanation as part b applies but here the price of y has changed.

Rahul Sunny answered 1 year ago

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