econ11_08_ps5_sol

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

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

View Full Document Right Arrow Icon
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? 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

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

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

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