Answer to Question #254074 in Economics of Enterprise for Ameli

Question

Suppose the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where p1,p2 > 0. a) Plot the indifference curves b) Find the Marshallian demand functions. Show graphically the utility maximizing choices.

Answer 1

a.

b.

$case \space 1\\U(X_1>X_2=X_1^2)\\MRS=\frac{MU_X1}{MU_X2}\\MU_X1=\delta X_1\\MU_X2=0\\ case \space 2\\U(X_1<X_2=X_2^2)\\MRS=\frac{MU_X1}{MU_X2}\\MU_X2=\delta X_1\\MU_X1=0$

$Budget \space constraint=P_1X_1+P_2X_2=W\\X_1(P_1+p_2)=W\\X_1=\frac{W}{p_1+p_2}\\ for \space X_2\\=P_1X_1+P_2X_2=W\\X_2(P_1+p_2)=W\\X_2=\frac{W}{p_1+p_2}$

c.