Question

A family has to decide how much of his monthly income to spend on Good 1 and Good 2. Suppose that this household has a fixed income of $600 per month. Further, suppose that the price of Good 1 is p1=$2 and the price of good 2 is p2=$1. Finally, suppose that the tastes of the households are described by utility function u(x₁,x_x2)= x₁^1/4x₂^3/4, where x1 denotes the quantity of Good 1 and x2 the quantity of Good 2.

Suppose that the government introduces a voucher system to support families whose monthly income is smaller than $1000. Vouchers have a dollar value that can be used to buy Good 1 as if the vouchers were cash, but the vouchers cannot be used for anything other than Good 1. Suppose that our family receives $300 of vouchers per month. What is the optimal quantity of Good 1 purchased by the family after the introduction of the vouchers?

Answer 1

Ans) without voucher the x1 if the whole amount is spend on good 1= 1/4x1*p1=600

X1= 600*4/2= 1200

While the whole amount is spend on good is = 600*4/3

= 800

Good 1purchased is 1200

Good 2 purchased is 800

Respectively if the whole amount is spend on one good only. While if the amount spend on both goods then the commodity purchased is = p1x1+ p2x2= m( budget line equation)

1/4*2+ 3/4*1=600

= 480

Total quantity of goods purchased is480.

Quantity purchased of x1= 120

X2= 360

Now if the voucher is given then the commodity purchased after voucher

Amount spend on good 1 is : 2*120= 240

Voucher Payment is = 300

Total increased amount = 540 to be spend on good 1

540/2 = quantity purchased by consumer

= 270

So the optimal amount which should be purchased of good 1 = 270.