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) 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 = , DP = % 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%
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This note was uploaded on 01/05/2012 for the course ECON 101 taught by Professor Gulipektunc during the Spring '11 term at Middle East Technical University.

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

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