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a06-part2 - Page 14 of 23 6 LABOUR SUPPLY AND INTERTEMPORAL...

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Unformatted text preview: Page 14 of 23 6. LABOUR SUPPLY AND INTERTEMPORAL CHOICE 6.1 (14) Labour Supply with Substitution Effect (SE) and Income Effect (IE) Myriam has a total of 24 available hours per day to devote to work or leisure. She is a doctor who is free to work as many hours as she likes per day at a wage of $50 per hour. Her indifference curves are convex and do not change throughout this question. a) (3) Use a fully labelled indifference curve diagram to show her equilibrium assuming she chooses to work 8 hours. Label it as point “A”. Myriam has recently given birth to a cute baby girl and somebody needs to take care of the baby. Myriam has two options: 0 Option One: She could hire a baby-sitter for $20 per hour and keep working.2 0 Option Two: She could stop working, take a maternity leave and receive compensation of $200 per day. b) (3) Is it possible that Myriam would stop working and take the maternity leave? (Yes / No). In the diagram below, illustrate your answer. 2 Myriam would need to hire the baby-sitter for a number of hours equal to the number of hours she is at work at the hospital (i.e., if Myriam works for 8 hours, she will hire the baby—sitter for 8 hours). C) d) Page 15 0f 23 (4) Quickly redraw the original equilibrium “A”. Suppose now that Myriam chooses to work for 10 hours per day (and hires the baby—sitter). Show her new equilibrium in the diagram below and label it as point “B”. Between A and B, I conclude that (the SE dominates the IE / the IE dominates the SE / the SE and IE work in the same direction) for Myriam. (Do NOT show SE and IE, but recall that leisure is assumed to be a “normal good”). Explanation (4) Quickly redraw Myriam's equilibrium “B” (when she is working 10 hours per day and employs the baby-stitter) on the diagram below. Myriam’s parents decide to help her out by giving her $100 per day. Show her new equilibrium on the diagram below, labelled as point “C”. I conclude she will now work (same / more / fewer) hours per day than at point B. Page 16 0f23 6.2 (6) Intertemporal Choice Assuming that current consumption and future consumption are normal goods and that there is no inflation, demonstrate in the diagram below that a saver may save less if the rate of interest increases. Show the Substitution Effect and the Income Effect in your answer. Use the Hicks Method. Provide a brief explanation of your diagram. Explanation: Phge17Qf23 7. PRICE INDEXES AND PERFECT COMPETITION 7.1 (10) Price Indexes Enrique spends his whole income on X and Y. In 2000, he bought 25 units of X at $8 each and 25 units of Y at $8 each. In 2006, he bought 40 units of X at $10 each and 10 units of Y at $20 each. a) (2) Compute the Laspeyres Price Index (LPI) for Enrique. LPI = b) (2) Compute the Paasche Price Index (PPI) for Enrique. PPI = c) (2) Using just the information above, and assuming no changes in preferences, what can we say about Enrique's situation in 2006 compared to 2000? He is (better off / worse off / equally well off / cannot determine). My conclusion is based on this statement about the change in prices and income: (1) (4) Use an indifference curve diagram to support your conclusion. (You need not show the intercepts for the budget lines, but you do need to show the position of each one, label as BLOO and BL06, and show the consumption points in 00 and 06). Page 18 on3 7.2 (10) Perfect Competition Cabbages are produced in a perfectly competitive industry. Assume firms have U-shaped cost curves. a) (4) In the diagram below for a representative firm, show an initial long run equilibrium. Provide both short run and long run average and marginal cost curves. Label the equilibrium as P;, Q. b) (4) Now consider a government intervention designed to assist cabbage growers to earn profits through an effective quota scheme. The scheme requires each firm to produce only 70% of the initial equilibrium amount. In the diagram above, show the new short run equilibrium. Assume no cheating on the quota amount. Be sure to show the profits area clearly. Label as P2, Q2. c) (2) [Instruction: Do NOT alter your diagram in any way to answer this question; just provide an explanation below.) Consider now the long run. Assume entry of new firms is not permitted and that there continues to be no cheating on the quota amount. Will there be any further adjustments in how the firm produces cabbages? (Yes / No). Explain briefly. Page 19 0f 23 8. MONOPOLY AND DUOPOLY The market demand schedule for good X is P = 58 - Q. Initially, a monopoly firm is the sole supplier of good X. The firm has a Total Cost function given by TC = $IOQ. a) (2) Calculate the following values for the profit-maximizing equilibrium. Quantit —— Consumer Surplus Monool Profits — b) (3) Suppose that the monopoly firm is able to practice perfect price discrimination (i.e., it is able to sell every unit for the highest price it could command). Calculate the following profit-maximizing values in these circumstances. Quantity Monopoly Profits — Consumer Surplus __ c) (3) Now assume the monOpoly firm is prohibited by law from price discrimination. Furthermore, it finds that a second firm has entered the market. Firm 2 has the same cost schedule as Firm 1, and it assumes that the first firm will continue to produce the quantity in part a) above. Calculate the following values when Firm 2 follows a profit-maximizing strategy. Price Firm 2 Quantity Firm 2 Profits Firm 2 Page 20 0f 23 d) (2) Firm 1 will respond to the entry of Firm 2. What is Firm’s 1’s Reaction Schedule if it always assumes that Firm 2 will keep its output constant? (Provide an equation, or illustrate in a diagram). Reaction Schedule: (equation, or diagram above) 6) (3) If both firms behave as simple Coumot duopolists, what is the equilibrium? Fill in the Table of Values below. Output of each Firm Price of X Profits of each Firm f) (4) Suppose now that Firm 2 realizes that Finn 1 will always react to whatever output Firm 2 produces. In other words, Firm 2 becomes a “smart” player while Firm 1 remains as a simple Coumot firm, as in the Stackelberg Model. Now fill in the Table of Values below when Firm 2 maximizes profits on this basis. i Price Firm 1 Price Firm 2 Quantity Firm 1 QuantitLF inn 2 Profits Firm 1 Profits Firm 2 g) Page 21 0f 23 (3) Firm 1 wakes up and its managers say, “surely it would be better for us if we could get Firm 2 to collaborate with us”. Indeed, the two firms reach an agreement to maximize aggregate profits and share output and profits equally. Fill in the Table of Values below describing this equilibrium. Outut of each Firm Price of X Profits of each Firm THE REST OF THIS PAGE IS BLANK Page 22 0f23 9. INPUT MARKETS 9.1 (10) Assume there is only one buyer of labour in a remote northern community in Ontario. Labour is the only variable input utilized by the firm, which sells in a competitive world market. For each case below, taken separately, use the diagram provided to demonstrate the impact on the quantity of labour employed and the wage rate per hour received by workers. Assume a positively sloped supply curve Of labour. [Since equations have not been provided, you are not expected to give precise answers; just label as L1, L2, etc] a) (5) A subsidy of $10 for each hour of labour employed. b) (5) An effective minimum wage, at a level higher than the non-regulated equilibrium. Will the firm always be able to obtain all the labour it wants, irrespective of the level of the minimum wage? (Yes / No) [Your diagram needs to demonstrate your answer, but no explanation is required]. Page 23 0f23 9.2 A firm has a production function of Q = ZKL. For this function, the MPL = 2K and a) b) MPK = 2L. The price of K is $20 per unit and the price of L is $10 per unit. (7) This production function exhibits (constant / increasing / decreasing) returns to scale. Returns to scale is a concept that applies in the (short run / long run / both short and long run). This production function (does / does not) exhibits the “law of diminishing returns” to labour (L). Diminishing returns is a concept that applies in the (short run / long run / both short and long run). In the long run, how many units of labour will the firm use per unit of capital, in order to maximize output for a given input budget? Number of units of labour (L) per unit of capital (K) = (3) One point on a (different) firm’s linear expansion path is K=l, L=1 at Q=10. In the diagram below, create an expansion path (EP) to demonstrate a production function that exhibits decreasing returns to scale. Show at least 3 points on the EP. ...
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