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# PS4_S - 1 METU Department of Economics Econ 101...

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Unformatted text preview: 1 METU Department of Economics Econ 101: Introduction to Economics I Sections 01-02-03 2011-2012 Fall Semester Problem Set 4 with SOLUTIONS (Ch. 5 and Appendix to Ch. 5 in Case et al.; and Relevant Parts of Ch. 5&amp;amp;6 in Lipsey et al.) PART A - QUESTIONS Q.1) You are given the demand functions for different five goods as follows: Q D1 = 8 - 2P Q D2 = 9 - 3P Q D3 = 10 - 4P Q D4 = 11 - 5P Q D5 = 12 - 6P a) Find the price and quantity where the price elasticity of demand equals one (unitary elasticity) for each demand functions. using the point elasticity, ε D = (∆ Q D / ∆P) *( P / Q) = -1 Q D1 = 8 - 2P , -2*( P / Q) = -1 , then 2P=Q , and then Q D1 = 8 – Q, Q=4, P=2 Q D2 = 9 - 3P , -3*( P / Q) = -1 , then 3P=Q , and then Q D2 = 9 – Q, Q=9/2, P=3/2 Q D3 = 10 - 4P , -4*( P / Q) = -1 , then 4P=Q , and then Q D3 = 10 – Q, Q=5, P=5/4 Q D4 = 11 - 5P , -5*( P / Q) = -1 , then 5P=Q , and then Q D3 = 11 – Q, Q=11/2, P=11/10 Q D5 = 12 - 6P , -6*( P / Q) = -1 , then 6P=Q , and then Q D3 = 12 – Q, Q=6, P=1 b) Over what ranges of prices are demand for each good elastic? Q D1 = 8 - 2P , elastic demand if p &amp;gt; 2 (or if 2 &amp;lt; p &amp;lt; 4) Q D2 = 9 - 3P , elastic demand if p &amp;gt; 3/2 (or if 3/2 &amp;lt; p &amp;lt; 3) Q D3 = 10 - 4P , elastic demand if p &amp;gt; 5/4 (or if 5/4 &amp;lt; p &amp;lt; 5/2) Q D4 = 11 - 5P , elastic demand if p &amp;gt; 11/10 (or if 11/10 &amp;lt; p &amp;lt; 11/5) Q D5 = 12 - 6P , elastic demand if p &amp;gt; 1 (or if 1 &amp;lt; p &amp;lt; 2) c) Over what ranges of prices are demand for each good inelastic? Q D1 = 8 - 2P , inelastic demand if p &amp;lt; 2 (or if 0 &amp;lt; p &amp;lt; 2) Q D2 = 9 - 3P , inelastic demand if p &amp;lt; 3/2 (or if 0 &amp;lt; p &amp;lt; 3/2) Q D3 = 10 - 4P , inelastic demand if p &amp;lt; 5/4 (or if 0 &amp;lt; p &amp;lt; 5/4) Q D4 = 11 - 5P , inelastic demand if p &amp;lt; 11/10 (or if 0 &amp;lt; p &amp;lt; 11/10) Q D5 = 12 - 6P , inelastic demand if p &amp;lt; 1 (or if 0 &amp;lt; p &amp;lt; 1) 2 Q.2) The following table shows the price and quantity of brownie in Basri’s canteen for a semester according to average income. Brownie price Quantity demanded (average income is 3000 TL in a semester) Quantity demanded (average income is 5000 TL in a semester) 1 TL 2400 3600 1.5 TL 1600 2800 2 TL 800 2400 2.5 TL 400 1800 a) Calculate the price elasticity of demand (using the midpoint method) if the price of brownies rises from 1 TL to 1.5 TL, when average income is 3000 TL. % Change in quantity demanded = (1600 – 2400) / ((1600 + 2400) / 2)*100% = – 40% % Change in price = (1.5 – 1) / ((1.5 + 1) / 2)*100% = 40% Price elasticity of demand = , D P = % Change in quantity demanded / % Change in price = – 1 b) Calculate the income elasticity of demand (using the midpoint method) if average income increases from 3000 TL to 5000 TL, when the price of a brownie is 1 TL. % Change in quantity demanded = (3600 – 2400) / ((3600 + 2400) / 2)*100% = 40% % Change in income = (5000 – 3000) / ((5000 + 3000) / 2)*100% = 50% Income elasticity of demand = , D Y = % Change in quantity demanded / % Change in income = 4/5 = 0.8....
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PS4_S - 1 METU Department of Economics Econ 101...

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