{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

View Full Document Right Arrow Icon
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...
Image of page 1

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

View Full Document Right Arrow Icon
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 . Rachel’s preferences are given by the Cobb-Douglas utility function: U ( R, S ) = R 0 . 1 S 0 . 1 . (a) Write out the Lagrangian for Rachel’s utility-maximization problem. (b) Use the Lagrangian to derive Rachel’s optimal bundle ( R * , S * ) which maximizes her utility. (c) For a given utility level, U 0 , find Rachel’s compensated demands for Rock Concerts and Sunglasses. You can use any method you want. (d) Use the compensated demands from part (c) to derive Rachel’s expenditure function E ( p R , p S , U 0 ). 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 ). (b) Suppose the firm wishes to produce 72 units of output. How much capital and how much labour does the firm employ? What is the long-run total cost of producing 72 units of output? (c) The firm suddenly decides to double the quantity of output but only has a day to complete the order. Therefore, in that time, the amount of capital is fixed at the level you found in part (b). The firm is free to adjust labour hours. How much will it cost to produce 144 units of output? (d) How much would it cost to produce 144 units of output if the firm could also vary capital? Is this cost higher or lower than the cost you found in part (c)? Explain. Question 3: Perfect competition [20 marks] Consider a competitive firm whose short-run cost function is C ( q ) = 5 + 5 q + 5 q 2 . However, all costs are non-sunk . The firm faces a market price of p for its output. (a) Derive the firm’s profit maximizing condition. Is the sufficient second-order condition satisfied?
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern