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2009-final-exam

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

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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...

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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?
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