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econ101_ps4_sol - METU Department of Economics Econ 101...

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METU Department of Economics Econ 101: Introduction to Economics I All sections (01-02-03) Fall 2010 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? P B = 8 YTL P B = 12 YTL P A Q A Q’ A Elasticity ( ε ) 8 2000 4000 1.67 7 4000 6000 1.00 6 6000 8000 0.71 ε 1 = % Change in quantity of “A” demanded = (4,000 – 2,000) / ((4,000 + 2,000) / 2) = 5 / 3 % Change in price B (12 – 8) / ((12 + 8) / 2) ε 2 = % Change in quantity of “A” demanded = (6,000 – 4,000) / ((6,000 + 4,000) / 2) = 1 % Change in price B (12 – 8) / ((12 + 8) / 2) ε 3 = % Change in quantity of “A” demanded = (8,000 – 6,000) / ((8,000 + 6,000) / 2) = 5 / 7 % Change in price B (12 – 8) / ((12 + 8) / 2) Since the cross elasticities are positive, we know that A and B are substitutes. 2. a) Calculate price elasticity of demand for the functions when P=8 and when P=6. i) P = 40 – 0.5Q or Q = 80 – 2P so uni2206 Q / uni2206 P = – 2 When P = 8, Q = 64, thus ε = – 0.25 where ε = ( uni2206 Q/ uni2206 P)*P/Q When P = 6, Q = 68, thus ε = – 0.176 ii) Q = – 4+0.75P uni2206 Q/ uni2206 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 uni2206 Q/ uni2206 P = -1 When P = 8, Q = 8 thus ε = -1 When P = 6, Q = 10 thus ε = -0.6
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b) Calculate the arc elasticity of demand between P = 6 and P = 8 for (ii) Q = – 4 + 0.75P When P = 8, Q = 2 & When P = 6, Q = 0.5 Arc elasticity of demand = % Change in quantity demanded = (2 – 0.5) / ((2 + 0.5) / 2) = 4.2 % Change in price (8 – 6)/ ((8 + 6)/2) 3. a) Find the equilibrium price and quantity. 100 – 2P = – 20+4P P* = 20 Q* = 60 b) Find the point elasticity of demand and supply at the equilibrium. ε D = uni2206 Q D / uni2206 P * P / Q = –2*20 / 60 = –2 / 3 ε S = uni2206 Q S / uni2206 P * P / Q = 4*20 / 60 = 4 / 3 c) Find the price and quantity where price elasticity of demand is unitary. ε D = uni2206 Q D / uni2206 P * P / Q D => –1 = –2* P / Q D => 2P = Q D & 2P+Q D = 100 Thus, 4P = 100 => P = 25 & Q = 50 d) Find the maximum expenditures by consumers (TR) given their demand. Max Expenditure by Consumers = 25 * 50 = 1,250 4. 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 ε = % 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 ε = % Change in quantity demanded / % Change in income = 1
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5. Use the given monthly information in the table to answer the questions below.
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