# FS08 - Economics 104A Solution for Final Exam Winter 2008 1...

• Notes
• jayrapkc
• 5

This preview shows pages 1–3. Sign up to view the full content.

Economics 104A Solution for Final Exam Winter 2008 1. Jerry consumes good 1 and good 2. His utility function is u ( x 1 , x 2 ) = x 1 - 1 x 2 . a) (6pt) Suppose initially ¯ p 1 = 4, ¯ p 2 = 4, and ¯ I = 100. Find the optimal bundle. Now suppose a quantity tax of \$1 is imposed on good 1. Find the substitution, income effect, and total effects of the quantity tax. The demand functions are x 1 ( p 1 , p 2 , I ) = I p 1 - s p 2 p 1 for good 1 and x 2 ( p 1 , p 2 , I ) = s p 1 p 2 for good 2 when p 1 p 2 I 2 . Using these demand functions, we get x * = ( x * 1 , x * 2 ) = (24 , 1) as the optimal bundle before tax. Next, the price of good 1 after tax is p 0 1 = 2 which implies Δ p 1 = p 0 1 - ¯ p 1 = 1. Hence, to calculate the (Slutsky) substitution and income effects, we need to increase Jerry’s income by Δ I = Δ p 1 x * 1 = 24, in order to make bundle x * affordable for him after tax. Using the demand functions again, y * = ( y * 1 , y * 2 ) = (24 . 8 - 0 . 8 , 1 . 25) is Jerry’s optimal bundle at p 0 1 , ¯ p 2 , I 0 = ¯ I + Δ I and z * = (20 - 0 . 8 , 1 . 25) if his optimal bundle at p 0 1 , ¯ p 2 , ¯ I . Thus, SE = y * 1 - x * 1 = 0 . 8 - 0 . 8 = - 0 . 09 and IE = z * 1 - y * 1 = - 4 . 8. Answer: b) (4pt) If the government asks Jerry at most how much of his income he would be willing to give up to prevent this quantity tax, what would his answer be, assuming he does not lie? Answer: Jerry’s utility level at optimal bundle after tax is 1 u ( z * ) = 20 - 2 0 . 8 . 1 u ( z * ) = z * 1 - 1 z * 2 = ¯ I p 0 1 - q ¯ p 2 p 0 1 - 1 q p 0 1 ¯ p 2 = ¯ I p 0 1 - 2 q ¯ p 2 p 0 1 . 1

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

Let I 0 denote income Jerry would need to achieve the above utility level if he could buy the goods at their initial levels. Then, from the demand functions, the optimal bundle would be y * = ( I 0 4 - 1 , 1) .
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