{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Midterm 1 Answers Continued

Midterm 1 Answers Continued - x 2 and less x 1 Technical...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
7. Answer. We are given: U ( x 1 ,x 2 ) = min( 1 3 x 1 ,x 2 ). These are Leontief preferences/perfect complements, so 1 3 x 1 = x 2 . Substitute into the budget constraint. p 1 x 1 + p 2 x 2 = M 3 p 1 x 2 + p 2 x 2 = M x 2 (3 p 1 + p 2 ) = M x * 2 = M (3 p 1 + p 2 ) We know that 1 3 x 1 = x 2 , so: x * 1 = 3 x * 2 = 3 M (3 p 1 + p 2 ) Alternatively, one could have substituted x 2 for x 1 in the beginning step, and arrive at the same answers. Common Errors Errors in basic algebra. (1-2 pts deducted, depending on severity of error.) Took Lagrangian of the min function. (No credit.) Rearranged budget constraint. (No credit.) Demand function was 1 3 x * 1 = x * 2 . (1 point credit, for realizing Leontief preferences/perfect complements.) 8. (Removed from exam.) Answer. We are given: MU 1 = 2 x 1 MU 2 = 3 x 2 p 1 = 4 p 2 = 1 1
Background image of page 1

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

View Full Document Right Arrow Icon
We want to know if the bundle (6 , 2) is optimal, and if not, find which direction to modify the bundle. Compare the MU p ratios to determine which good gives the most marginal utility per dollar. MU 1 p 1 = 2 * 6 4 = 3 MU 2 p 2 = 3 * 2 1 = 6 MU 2 p 2 > MU 1 p 1 x 2 generates more marginal utility per dollar spent on it, so we conclude that we must purchase more
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x 2 and less x 1 . Technical aside. Many students tried to use the first order conditions MRS = p 1 p 2 to find the optimal bundle. What they failed to realize was that the preferences were not convex. To find the original optimal bundle, we integrate over the marginal utilities of both goods, separately. U ( x 1 ,x 2 ) = Z MU 1 dx 1 = Z 2 x 1 dx 1 = x 2 1 + c 1 U ( x 1 ,x 2 ) = Z MU 2 dx 2 = Z 3 x 2 dx 2 = 3 2 x 2 2 + c 2 So, we conclude that: U ( x 1 ,x 2 ) = x 2 1 + 3 2 x 2 2 + c Where c , c 1 , c 2 are arbitrary constants. The indifference curves of this utility function are elliptical, centered around the origin. It is clear then that preferences are not convex, so the first order conditions MRS = p 1 p 2 cannot be used. (Nonconvex preferences imply that points of tangencies are local minima, not maxima.) 2...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

Midterm 1 Answers Continued - x 2 and less x 1 Technical...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online