Question

5. Suppose that an individual’s utility is given by ?(?, ?) = ?^(1/4)? ^(3/4). Let I denote income, ?? the price of x, and ?? the price of y.

e. Suppose the price of good x is $0.25 and the price of good y is $0.75. How much money would this individual need to spend to reach a utility level of 10? (Show your work and provide a numerical answer.) (6 points)

f. Suppose that the price of good x increases to $1.00 and the price of good y remains unchanged. How much worse off would this individual be? Write down an expression to quantify this welfare loss in terms of a monetary value.

Answer 1

5(e) This can be found using expenditure function.Expenditure function shows minimum expenditure required to achieve a given utility level for a particular set of prices.

In this question expenditure function is E= 1.74 Px^1/4* Py^3/4 *V

Plug in value of Px,Py and V in this equation to get E=10.

So he needs 10 dollars to reach utility level of 10.

5(f) If Px increases to 1 then to achieve same level of utility(10) ,it needs income:

E= 1.74 Px^1/4* Py^3/4 *V=14

So he needs 4 additional dollars to achieve the same level of utility that he was getting before.

Hence we have quantified welfare loss in terms of monetary value.