Question

A consumer has preferences given by U(x, y) = min[x, y].
(a) Calculate the equilibrium quantities of x and y when px = $2, py = $3
and I = 12.
(b) Suppose px increases to $3 when a per unit tax of $1 is placed on x.
What is the new value of x and how much tax revenue is raised?
(c) Suppose that the same tax revenue is raised by an income tax as
opposed to a per unit tax. Show that in this example the consumer
is no better off with the income tax.

Answer 1

Given the preference U(x,y)=min[x,y] and the budget constrain

2x+3y=12

a. At equlibrium the consumer will consume same amount of x as y

i.e x=y

putting the equation in the budget constrain we get

So at eqlibrium the consumer will consume 2.4 units of X and 2.4 units of Y.

b. Now the Px increases to $3 due to increse in $1 tax

so the new budget constrain become

As per the preferrence the consumer will consume same amout of X as Y

i.e

So at equlibrium X=Y=2

As the consumer will consume two units of X the tax revenue will be raised by $2.

c. Now, $1 charged from the income then the new budget constrain will be

So the equlibrium X=Y

Now the no of unit consumed is X=Y=2.2