2009-final-answers

2009-final-answers - EXAMINATIONS 2009 TRIMESTER 1 ECON 201...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: EXAMINATIONS 2009 TRIMESTER 1 ECON 201 MICROECONOMICS Time allowed: THREE HOURS Instructions: This is a closed book exam Answer ANY FIVE of the eight questions below Each problem is worth 20 marks You can use non-programmable calculators Please show your working ECON 201 Continued. . . Question 1: Consumer choice [20 marks] Rachel spends her income, Y , on Rock Concerts ( R ) and Sunglasses ( S ). Their prices are p R and p S . Rachels preferences are given by the Cobb-Douglas utility function: U ( R,S ) = R . 1 S . 1 . (a) Write out the Lagrangian for Rachels utility-maximization problem. leaf leaf The Lagrangian for Rachels utility maximization problem is leaf L = R . 1 S . 1 + ( Y p R R p S S ) . (b) Use the Lagrangian to derive Rachels optimal bundle ( R * ,S * ) which maximizes her utility. leaf leaf The first-order conditions are leaf L R = 0 . 1 R- . 9 S . 1 p R = 0 L S = 0 . 1 R . 1 S- . 9 p S = 0 leaf and leaf L R = Y p R R p S S = 0. leaf Rearrange and divide the first two conditions to get leaf MU R MU S = S R = p R p S . leaf Thus, p R R = p S S . After substituting in the third first-order condition, we obtain leaf S = . 5 Y p S , R = . 5 Y p R . (c) For a given utility level, U , find Rachels compensated demands for Rock Concerts and Sunglasses. You can use any method you want. leaf leaf To calculate the compensated demands, we use the following pair of conditions: leaf MU R MU S = S R = p R p S leaf and leaf R . 1 S . 1 = U . leaf From the first condition, we get R = p S S/p R . Substitute in the constraint to get leaf parenleftbigg p S p R parenrightbigg . 1 S . 2 = U . leaf Therefore, leaf S = U 5 parenleftbigg p R p S parenrightbigg . 5 . leaf Similarly, we get leaf R = U 5 parenleftbigg p S p R parenrightbigg . 5 . ECON 201 2 Continued. . . (d) Use the compensated demands from part (c) to derive Rachels expenditure function E ( p R ,p S ,U ). leaf leaf The expenditure function is leaf E ( p R ,p S ,U ) = p R R + p S S = p R U 5 parenleftbigg p S p R parenrightbigg . 5 + p S U 5 parenleftbigg p R p S parenrightbigg . 5 = 2 p R p S ( U ) 5 . Question 2: Short run versus long run costs [20 marks] A firm produces output according to the following production function: q = f ( L,K ) = L 1 / 3 K 2 / 3 . The cost of labour w is $ 27 per hour and the rental cost of capital r is $ 2 per hour. (a) With the given prices, compute the cost-minimizing capital-to-labour ratio ( K/L ). leaf leaf The cost-minimizing input bundle satisfies leaf MP L MP K = (1 / 3) L- 2 / 3 K 2 / 3 (2 / 3) L 1 / 3 K- 1 / 3 = w r = 27 2 , leaf This condition simplifies to leaf 1 2 K L = 27 2 ....
View Full Document

This note was uploaded on 05/24/2011 for the course ECON 201 taught by Professor Paulclacott during the Fall '10 term at Victoria Wellington.

Page1 / 9

2009-final-answers - EXAMINATIONS 2009 TRIMESTER 1 ECON 201...

This preview shows document pages 1 - 4. Sign up to view the full document.

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