econ11_08_ps5_sol

# econ11_08_ps5_sol - Eco11 Fall 2008 Simon Board Economics...

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

Eco11, Fall 2008 Simon Board Economics 11: Solutions to Practice Problems 5 (Week 6) November 4, 2008 1. Complements and Substitutes Suppose u ( x 1 , x 2 ) = x 1 x 2 . Are x 1 and x 2 gross complements or substitutes? Are they net complements or substitutes? Solution Marshallian demand is given by x * 1 = m/ 2 p 1 and x * 2 = m/ 2 p 2 . Since demand for good i is independent of p j these are neither gross complements or gross substitutes. Hicksian demand is given by h 1 = ( up 2 /p 1 ) 1 / 2 and h 2 = ( up 1 /p 2 ) 1 / 2 . Since h i is increasing in p j , these goods are net substitutes. 2. Choice with Partial Subsidies Suppose an agent chooses how much bread, x 1 , and wine, x 2 , to consume. The agent views the goods as perfect substitutes and has utility function: u ( x 1 , x 2 ) = x 1 + x 2 The price of bread is p 1 = 4, while the price of wine is p 2 = 2. The agent has income m = 4. (a) Solve for the agent’s optimal consumption. (b) In order to encourage the consumption of bread, the Government subsidises the first unit by \$1. Hence the first unit costs p 1 = 3, while each unit thereafter costs p 1 = 4. (i) Draw the agent’s budget constraint. (ii) Solve for her optimal consumption. (iii) How much does the subsidy cost the Government? (c) The Government increases it’s subsidy on the first unit to \$3. Hence the first unit costs p 1 = 1, while each unit thereafter costs p 1 = 4. (i) Draw the agent’s budget constraint. (ii) Solve for her optimal consumption. (iii) How much does the subsidy cost the Government?

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