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Assignment2ans - ASSIGNMENT 2 Economics 203 Fall 2011 Due...

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ASSIGNMENT 2 Economics 203 Fall 2011 Due: Friday Nov 4th, 2011 at 3:00 pm . The assignment is out of 100 marks and counts towards 9% of your final grade. If you work with others, please indicate their names in the top right-hand corner of your assignment (you will not be penalized). In any event, write up the work on your own. Copying will be considered cheating. Question 1 (25 marks): A firm has two plants that produce identical output. The cost functions are 2 3 1 2 3 2 1: 10 4 2: 10 2 Plant C Q Q Q Plant C Q Q Q a) Derive the average total cost function, marginal cost function, variable cost function and fixed cost function (if exists) for plant 1. (5 marks) For plant 1: ATC 1 = TC 1 /Q 1 => 2 1 1 1 10 4 ATC Q Q MC 1 = 2 1 1 1 1 10 8 3 TC Q Q Q 2 3 1 1 1 1 10 4 VC Q Q Q There is no fixed cost. b) Derive the average total cost function, marginal cost function, variable cost function and fixed cost function (if exists) for plant 2. (5 marks) For plant 2: ATC 2 = TC 2 /Q 2 => 2 2 2 2 10 2 ATC Q Q MC 2 = 2 2 2 2 2 10 4 3 TC Q Q Q 2 3 2 2 2 2 10 2 VC Q Q Q There is no fixed cost. c) At what output levels does the average cost curve of each plant reach its minimum? (5 marks) For plant 1: Min ATC 1 => 1 1 1 1 4 2 0 2 ATC Q Q Q Q 1 =2 is the minimum point on the ATC 1 curve as 2 1 2 1 2 0 ATC Q Min ATC 2 => 2 2 2 2 2 2 0 1 ATC Q Q Q
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Q 2 =1 is the minimum point on the ATC 2 curve as 2 2 2 2 2 0 ATC Q d) Show that the marginal cost is equal to the average cost at the minimum point on the average cost curve. (5 marks) MC 1 = ATC 1 => 2 2 1 1 1 1 10 8 3 10 4 Q Q Q Q 1 1 2 ( 2) 0 Q Q Q 1 =0 or Q 1 =2. The MC curve crosses the ATC curve at 2 points corresponding with values of quantity. One is when at Q 1 =0 as there is no fixed cost. The other is at the ATC minimum point where Q 1 =2.
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