Midterm%20Exam_Key

# Wn n 65 035 2k π w n dn d π k w n d 35 1 3 1 we

This preview shows pages 5–8. Sign up to view the full content.

= wN N 65 . 0 0.35 2K π = = 0 2(0.65)K 35 . 0 0.35 w N dN d π K w N d 35 . 0 1 3 . 1 = . We need to also calculate profits: wN N w w N w N ) 5384 . 0 ( ) K ) 65 . 0 ( 2 2K ( ) 2K ( 0.35 0.35 35 . 0 0.35 = = = π π π . Now we have enough information to solve the general equilibrium. First, use the profit equation in the labor supply: N N N N w wN N s s s ) 4038 . 0 ( 6 ) 5384 . 0 ( (0.75) 6 ) 5384 . 0 ( (0.75) 6 = = = Given that at equilibrium, d s N N = 27 . 4 6 ) 4038 . 1 ( ) 4038 . 0 ( 6 * = = = N N N N (2 points) Using this information at K w N d 35 . 0 1 3 . 1 = implies . (2 points) 0309 . 3 * = w The rest can be calculated by substitution: 968 . 6 * = π (2 points) 73 . 19 * = l (2 points) 93 . 19 * = C (2 points) 93 . 19 * = y (2 points) 97 . 19 * = u (3 points) 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Izmir Univery of Economics I. Hakan Yetkiner Department of Economics Social Planner’s Problem: For this approach, we setup the following problem: The Lagrange is: { } 65 . 0 35 . 0 75 . 0 0.25 2 C N K C l L λ = . The first order conditions are: 0 C ) 25 . 0 ( 0 75 . 0 0.75 - = = λ l C L (Equation 1) { } 0 ) 1 ( ) ( ) 65 . 0 ( 2 C ) 75 . 0 ( 0 35 . 0 35 . 0 25 . 0 0.25 = λ = l h K l l L (Equation 2) 65 . 0 35 . 0 2 0 N K C L = = λ (Equation 3) (Deriving the first-order conditions is 3 points) From the first two first-order conditions (i.e., from (1) and (2)), we obtain: l l C l l l 35 . 0 35 . 0 25 . 0 0.25 75 . 0 -0.75 ) 24 )( 679 . 1 ( ) 24 )( 039 . 5 ( 1 C ) 75 . 0 ( C ) 25 . 0 ( = = Using this result for C in the third first-order condition: = 65 . 0 35 . 0 ) 24 )( 75 . 7 ( ) 24 )( 679 . 1 ( l l l (2 points) 73 . 19 * = l The rest follows from substitution: 27 . 4 * = N (2 points) 93 . 19 * = C (2 points) 93 . 19 * = y (2 points) 97 . 19 * = u (3 points) Note that we do not have and in the social planner’s problem. * w * π 6
Izmir Univery of Economics I. Hakan Yetkiner Department of Economics 5 . ( 10 Points ) Suppose that Daniel has income of y 1 when he is young and y 2 when he is old. The real interest rate is 1 = r . The overall utility function of Daniel is . 5 . 0 2 5 . 0 1 2 ) 5 . 0 ( 2 c c U + = (i) Find the optimal values of , and .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern