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Unformatted text preview: ANSWERS to Questions 45/Discussion 2 Answer to Q.4 a) Using the logarithm function we transform the utility function as follows: V ( x1 , x2 ) = ln( x13 x 1 ) = 3 ln x1 + ln x 2 2
Hence, MRS = MU 1 3 x1 3x2 = = MU 2 1 x2 x1 b) MRS at (1,1) is 3. c) The first condition is the budget line: 40 x1 + 20 x 2 = 800 2 x1 + x 2 = 40 . The second is the optimality condition: MRS1, 2 = 3x P1 40 3x2 = 2 x1 . 2 = x1 20 P2 d) First we solve for x2 using the budget line, and then we plug x2 into the optimality condition to find x1. The optimal bundle is (x1 ,x2) = (15, 10), which is interior. ANSWER to Q.5 a) b) U ( x1 , x 2 ) = x1 + x 2 U ( x1 , x 2 ) = a ( x1 + x 2 ) + b, a, b > 0 U ( x1 , x 2 ) = ln( x1 + x 2 ) U ( x1 , x 2 ) = ( x1 + x 2 ) 2 c) MU1=1, MU2=1. So, MRS=1. MRS does not depend on x1 or x2. The two goods are perfect substitutes, hence, the MRS is the same at any point on the IC. d) Budget Line: 2 x1 + x 2 = 100 . See figure 5. (x1*,x2*)=(0,100), which is a corner solution. e) Budget Line: x1 + 2 x 2 = 100 . See figure 6. (x1*,x2*) = (100,0), which is a corner solution. f) Budget Line: x1 + x 2 = 100 . See figure 7. Any choice on the budget line is optimal. ...
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