Answer to Question #207623 in Microeconomics for jay

Question #207623

1.    If an individual’s preferences are described by the utility function U(X1 , X2 ) = X12 + X22,

a)    graph the indifference curve for U = 20 and U= 40.

b)    Find the optimal consumption quantities if P1 = US$2.50 ;                     P2 = US$ 7.50; and M = US$ 60.


1
Expert's answer
2021-06-17T12:39:33-0400

Part a

U(X1 , X2 ) = X12 + X22

The indifference curve is as shown below


If P1=2.5;P2=2.5;m=60P_1=2.5; P_2=2.5; m=60 , the budget line will be as follows

P1x1+P2x2=mP_1x_1+P_2x_2 =m

2.5x1+2.5x2=602.5x_1+2.5x_2 =60

Also from U(X1 , X2 ) = X12 + X22

MR(x1,x2)=mUx1mUx2MR_{(x_1,x_2)}=\frac{mUx_1}{mUx_2} as mUx1=2x1&mUx2=2x2mUx_1 = 2x_1 \& mUx_2 = 2x_2

So, MR(x1,x2)=2x12x2=x1x2MR_{(x_1,x_2)}=\frac{2x_1}{2x_2} =\frac{x_1}{x_2}


Part b

Equating the slope of budget line and MRs

P1P2=MRs(x1,x2)    2.57.5=x1x2\frac{P_1}{P_2} =MRs_{(x_1,x_2)} \implies \frac{2.5}{7.5}=\frac{x_1}{x_2}

x2=3x1x_2=3x_1

Therefore, 2.5x1+7.5(3x1)=60    x1=6025=2.4;x2=7.22.5x_1+7.5(3x_1)=60 \implies x_1= \frac{60}{25}=2.4; x_2= 7.2


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