PS8_S - 1/7 METU Department of Economics Econ 101 Sections...

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Unformatted text preview: 1/7 METU Department of Economics Econ 101 Sections 01 – 02 – 03 Fall 2011 PROBLEM SET # 8 (with Answers) (Chapters 12 & 13) PART A – PROBLEMS: 1. A monopoly’s cost and revenue structure is given below: Q P = AR TR MR TC MC PROFIT 0 51 0 - 4 -4 1 46 46 46 34 30 12 2 41 82 36 59 25 23 3 36 108 26 80 21 28 4 31 124 16 96 16 28 5 26 130 6 114 18 16 6 21 126 -4 135 21 -9 7 16 112 -14 160 25 -48 8 11 88 -24 189 29 -101 9 6 54 -34 222 33 -168 10 1 10 -44 259 37 -249 a) Fill the blank cells. b) Monopoly’s equilibrium price is 31 . c) Monopoly’s equilibrium quantity is 4 . d) Profit/Loss at equilibrium is 28 . e) Show equilibrium price, quantity and profit/loss on the relevant diagram(s). 2. A monopolist’s average revenue function: P = 120 – 2Q It also knows that its fixed cost is 100. The AVC is represented as AVC = 60 + 2Q a) Find the total revenue (TR) function. Since ¡ ¢ £¤ ¥¡ ¢ £ ¦ § ¢ ¨©ª«¬– ¬ª§­ ¦ § ¢ ©ª«§¬– ¬ª§ ª b) Find the MR and MC function. ¥® ¢ ¥¯® ° ¥±® ¢ ©«« ° ±® ¦ §¬¬¬¬ ¢² ¬¬¬¬¥® ¢ ©«« ° ³«§ ° ª§ ª ´® ¢ µ¥®¶µ§ ¢ ³« ° ·§¬¬¬¬¬¬¸ ¬¬¬¬¬´¡ ¢ µ¥¡¶µ§ ¢ ©ª«¬– ¬·§¬ 2/7 c) Find the quantity that gives the maximum TR. Total revenue is maximized when its first derivative with respect to quantity (i.e. marginal revenue) is equal to zero. Total revenue is also maximized when elasticity of demand is equal to one; i.e. mid- point of the demand curve. ¡¢£– £¤¥ ¦ ¢££££££ ¦§ £££££¥ ¦ ¨¢ d) Find the quantity that gives the minimum AC. Average cost is minimized when its first derivative with respect to quantity is equal to zero. Alternatively, average cost is minimized when AC = MC. ©ª ¦ «ª¬¥ ¦ ­ ¢¢¬¥® ¯ °¢ ¯ ¡¥££££ ¦§ £££±©ª¬±¥ ¦ ¡£–£­ ¢¢¬¥ ¡ ® ¦ ¢£££ ¦§ ££¥ ¦ √²¢ e) Determine the profit maximizing level of output and find the profit. Profit is maximized when marginal revenue and marginal cost is equal to each other. °¢ ¯ ¤¥ ¦ ¡¢£– £¤¥££££ ¦§ ££ ¥ ³´µ´¶´·¸ ¹ ¦ º» ² «¼ ¦ ¡¢¥£– ¡¥ ¡ ¦ ²º²¬¡££££££££££½ ££££«¾ ¦ ¢¢ ¯ °¢¿ ¯ ¡¿ ¡ ¦ ¨¡²¬¡££ ÀÁ´ÂÃÄ ¦ «¼£– £«ª ¦ ¡²£ f) What would the profit maximizing level of output be if this market is perfectly competitive? Under perfect competition, profit maximization implies À ¦ ³ª» To obtain perfectly competitive outcome, ¡¢ Å ¡¥ ¦ °¢ ¯ ¤¥££ ¦§ ££££ ¥ ÀÆÁÂÆÇÄ·¸ ¹ ¦ ¢ ....
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PS8_S - 1/7 METU Department of Economics Econ 101 Sections...

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