econ101_ps4_sol - METU Department of Economics Econ 101...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 u Q / u P = – 2 When P = 8, Q = 64, thus ε = – 0.25 where ε = ( u Q/ u P)*P/Q When P = 6, Q = 68, thus ε = – 0.176 ii) Q = – 4+0.75P u Q/ u 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 u Q/ u P = -1 When P = 8, Q = 8 thus ε = -1 When P = 6, Q = 10 thus ε = -0.6
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 = u Q D / u P * P / Q = –2*20 / 60 = –2 / 3 ε S = u Q S / u P * P / Q = 4*20 / 60 = 4 / 3 c) Find the price and quantity where price elasticity of demand is unitary. ε D = u Q D / u P * P / Q D => –1 = –2* P / Q D => 2P = Q D 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%
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

econ101_ps4_sol - METU Department of Economics Econ 101...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online