Question

Andy is indifferent between consuming M units of x or N units of y. Which of the following utility functions of x and y can represent Andy’s preference?

(a) U(x,y)=Mx+Ny

(b) U(x,y)=ln(Nx+My)

(c) Both of the above

(d) None of the above

Answer 1

The correct answer is (b) U(x,y)=ln(Nx+My)

It is given that Andy is indifferent between consuming M units of x or N units of y. This means his utility if he consumes only M unit of x = utility if he consumes only N unit of y

In option (a) U(x,y)=Mx+Ny , If he consumes M unit of x(and 0 units of y) then his utility(U) = M*M+N*0 = M² and If he consumes N units of y(and 0 units of x) then his utility(U) = M*0+N*N = N²

Hence, Andy is indifferent between consuming M units of x or N units of y if M² = N²

Here it is not given that M = N(more precisely there is no relation between M and N is mentioned) hence we cannot say about option (a) and hence option (a) is incorrect

In option (a) U(x,y)=ln(Nx+My) , If he consumes M unit of x(and 0 units of y) then his utility(U) = ln(N*M+M*0) = ln(NM) and If he consumes N units of y(and 0 units of x) then his utility(U) = ln(N*0+M*N = ln(NM)

Thus, his utility if he consumes only M unit of x = utility if he consumes only N unit of y {Note both equals ln(NM)}

So, only option (b) is correct.

Hence, the correct answer is (b) U(x,y)=ln(Nx+My)