PS4&Answers - METU Department of Economics Econ 101...

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1 METU Department of Economics Econ 101 Introduction to Economics I All sections Fall 2009 PROBLEM SET # 4 (With Answers) (CHAPTER 5 and Relevant Parts of Chapters 5&6 in Lipsey et al.) PART A: PROBLEMS 1. The table below gives the demand schedules for good A when the price of good B (P B ) is 8 YTL and 12 YTL. Complete the last column of the table by computing the cross elasticity of demand between goods A and B for each of the three prices of A. Are A and B complements or substitutes? (Use mid-point(arc-elasticity) formula) P B = 8 YTL P B = 12 YTL P A Q A Q’ A Elasticity 8 2000 4000 1.67 7 4000 6000 1.00 6 6000 8000 0.71 Cross price elasticity of demand = % Change in quantity demanded of good A % Change in price of good B (4000 2000) / ((4000 + 2000) / 2) = 0.667 = 1.67 (12 8) / ((12 + 8) / 2) 0.4 (6000 4000) / ((6000 + 4000) / 2) = 0.4 = 1.00 (12 8) / ((12 + 8) / 2) 0.4 (8000 6000) / ((8000 + 6000) / 2) = 0.286 = 0.715 (12 8) / ((12 + 8) / 2) 0.4 Since the cross price elasticities are positive, we know that A and B are substitutes.
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2 2. i. P = 40 0.5Q ii. Q = -4 + 0.75P iii. 4Q + 4P = 64 a. Calculate price elasticity of demand or supply for the functions (i), (ii), (iii) when P=8 and when P=6. b. Calculate the arc elasticity of demand between P=6 and P=8 for (i) a. i) P = 40-0.5Q or 0.5Q = 40-P thus Q = 80- 2P so ∆Q/ ∆P = -2 When P = 8, Q = 64, thus ε = -0.25 where ε = (∆Q/∆P)*P/Q When P = 6, Q = 68, thus ε = -0.176 ii) Q = - 4+0.75P → ∆Q/∆P = 0.75 When P = 8, Q = 2 thus ε = 3 When P = 6, Q = 0.5 thus ε = 9 iii) 4Q + 4P = 64 thus Q = 16 P so ∆Q/∆P = -1 When P = 8, Q = 8 thus ε = -1 When P = 6, Q = 10 thus ε = -0.6 b. P = 40 - 0.5Q When P = 8, Q = 64 and when P = 6, Q = 68 Arc elasticity of demand = % Change in quantity demanded = (64 68) / ((64 + 68) / 2) = -0.106 % Change in price (8 6)/ ((8 + 6)/2)
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3 3. The following table shows the price and yearly quantity of T-shirts according to average income. T-shirt price Quantity demanded (average income is $20,000) Quantity demanded (average income is $30,000) $4.50 2,400 3,600 $5.50 1,600 2,800 $6.50 800 2,400 $7.50 400 1,800 a. Calculate the price elasticity of demand (using the midpoint method) when the price of T- shirts rises from $4.50 to $5.50, when average income is $20,000. % Change in quantity demanded = (1,600 2,400) / ((1,600 + 2,400) / 2)*100% = 40% % Change in price = (5.5 4.5) / ((4.5 + 5.5) / 2)*100% = 20% Price elasticity of demand = , D P = % Change in quantity demanded / % Change in price = 2 b. Calculate the income elasticity of demand (using the midpoint method) when average income increases from $20,000 to $30,000, when the price of a T-shirt is $4.50. % Change in quantity demanded = (3,600 2,400) / ((3,600 + 2,400) / 2)*100% = 40% % Change in income = (30,000 20,000) / ((30,000 + 20,000) / 2)*100% = 40% Income elasticity of demand = , D Y = % Change in quantity demanded / % Change in income = 1. 4. The market demand and supply curves for good X are as follows: Q = 50 (1/2)P and Q = - 40/3 + (1/3)P (P is in $ per unit) a) Find the equilibrium price and quantity. b) What is the equilibrium price and quantity due to a tax of $5 per unit on producers? c) What is the arc elasticity of demand between the initial and after tax equilibria? Is total revenue at the after tax equilibrium higher or lower than at the before tax equilibrium?
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