Summer CH1 Solutions

Summer CH1 Solutions - MIME 310 ENGINEERING ECONOMY...

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1 M I M E 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM EXERCISES – INTRODUCTION 1. i) The demand curve for the commodity is shown below. ii) For a demand schedule, the arc elasticity (AE) is given by: AE D = -{(Q 2 – Q 1 ) / [(Q 1 + Q 2 ) / 2]} / {(P 2 - P 1 ) / [(P 1 + P 2 ) / 2]} in which the subscripts 1 and 2 represent the extremities of the arc. Simplifying: AE D = -[(Q 2 - Q 1 ) / (Q 1 + Q 2 )] / [(P 2 - P 1 ) / (P 1 + P 2 )] For the arc associated with the $14.0-14.5/kg price interval, P 1 =14.0, Q 1 =48 640 and P 2 =14.5, Q 2 =47 200 (Q expressed in thousands); thus, AE D = -[(47 200 - 48 640) / (48 640 + 47 200)] / [(14.5 - 14.0) / (14.0 + 14.5)] = -(-1440 / 95 840) / (0.5 / 28.5) = 0.0150 / 0.0175 = 0.857 The results for the other price intervals are given in the table below. 12 14 16 18 20 22 30 35 40 45 50 55 QUANTITY ('000 000 kg/yr) PRICE ($/kg) Demand
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2 Price Interval ($/kg) Q 1 (10 3 kg/yr) Q 2 (10 3 kg/yr) AE D 14.5 - 15.0 47 200 45 800 0.888 15.0 - 15.5 45 800 44 440 0.919 15.5 - 16.0 44 440 43 120 0.950 16.0 - 16.5 43 120 41 840 0.979 16.5 - 17.0 41 840 40 600 1.008 17.0 - 17.5 40 600 39 400 1.035 17.5 - 18.0 39 400 38 240 1.061 18.0 - 18.5 38 240 37 120 1.085 18.5 - 19.0 37 120 36 040 1.107 19.0 - 19.5 36 040 35 000 1.127 19.5 - 20.0 35 000 34 000 1.145 The price elasticity of demand increases as the price increases. For the demand curve used here, the elasticity of demand is below unity (i.e. inelastic) at low prices, and above unity (i.e. elastic) at high prices . The elasticity is unitary at mid-range, either at the high end of the $16.0-16.5/kg price interval or at the low end of the $16.5-17.0/kg price interval. This behaviour is typical of most demand functions. 2. The total consumer expenditure (P • Q) associated with the demand schedule is given in the table below and plotted as a function of price in the diagram that follows. A smooth curve has been drawn through the values. The total consumer expenditure is maximized at a price of ap- proximately $16.60/kg . This is the price at which the elasticity of demand is unitary , confirming the observation made above. Price ($/kg) Total Consumer Expenditure ('000 $) 14.0 680 960 14.5 684 400 15.0 687 000 15.5 688 820 16.0 689 920 16.5 690 360 17.0 690 200 17.5 689 500 18.0 688 320 18.5 686 720 19.0 684 760 19.5 682 500 20.0 680 000
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3 3. i) The supply curve for the commodity is shown below, along with the demand curve from problem 1. 12 14 16 18 20 22 30 35 40 45 50 55 QUANTITY ('000 000 kg/yr) PRICE ($/kg) Demand Supply Market equilibrium 675 680 685 690 695 13 14 15 16 17 18 19 20 21 PRICE ($/kg) TOTAL CONSUMER EXPENDITURE ('000 000 $)
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4 ii) For a supply schedule, the arc elasticity (AE) is given by: AE S = {(Q 2 – Q 1 ) / [(Q 1 + Q 2 ) / 2]} / {(P 2 - P 1 ) / [(P 1 + P 2 ) / 2]} in which the subscripts 1 and 2 represent the extremities of the arc. Simplifying:
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.

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Summer CH1 Solutions - MIME 310 ENGINEERING ECONOMY...

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