3 Assume Matts utility function is given by ux1x2min T22The

3. Assume Matt\'s utility function is given by u(x1,x2)-(min ,T2})2·The prices of goods 1 and 2 are pi and p2, respectively, and his income is m (a) What kind of preference does this utility function represents? (b) Find the optimal levels of consumption for goods 1 and 2.

Solution

a) Given Preferences are continuous, Locally non satiated, Twice differentiable. we can work out 2 different cases,

1) x1>x2, 2) x2>x1

In 1st Case U(x1,x2)=x2^2 and In 2nd Case U(x1,x2)=x1^2

b)

In 1st case

we will use maximisation methods

Z= U(x1,x2)-Lambda(M-p1x1-p2x2)

dZ/dx1=-Lambda(p1); dZ/dx2=2x2-Lambda*p1 these FOC conditions dZ/dx1=0 ; dZ/dx2=0

2*x2/p1=Lambda. In this case utility doesnt change with x1

x2=Lambda*p1/2

In case 2

2*x1/p2=Lambda in this case utility doesnt change with x2

x1=Lambda*p2/2