PS4_AK - 100A PS4 KEY April 7 2013 Question 1 Part a Directly from the production function we see that F = 4000 V C = 3000Q 4000 AF C = Q 3000Q AV C =

PS4_AK - 100A PS4 KEY April 7 2013 Question 1 Part a...

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100A PS4 KEY April 7, 2013 Question 1 Part a) Directly from the production function we see that F = 4000. V C = 3000 Q - 4 Q 2 + 0 . 8 Q 3 AFC = 4000 Q AV C = 3000 Q - 4 Q 2 + 0 . 8 Q 3 Q ATC = AFC + AV C MC = @ 3000 Q - 4 Q 2 + 0 . 8 Q 3 @ Q = 3000 - 8 Q + 2 . 4 Q 2 Part b) We have the usual graph; 1
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Part c) MC = AV C 3000 - 8 Q + 2 . 4 Q 2 = 3000 - 4 Q + 0 . 8 Q 2 Q = 2 . 5 MC = 2995 This is the shutdown price. The plant only enters the market when price is greater than 2995, its marginal cost of production. Part d) Note that the price is higher than 2995; the shutdown price we found above. Thus it will produce. We know that above the shutdown price MC is the supply curve. So solve for Q from; 3000 - 8 Q + 2 . 4 Q 2 = 3000 ) Q = 3 . 33 Part e) Solve Q in terms of price p from the MC . p = 3000 - 8 Q + 2 . 4 Q 2 0 = 2 . 4 Q 2 - 8 Q + (3000 - p ) Q = 8 ± p 64 - 4 2 . 4 (3000 - p ) 2 2 . 4 ) Q = 8 + p 64 - 4 2 . 4 (3000 - p ) 2 2 . 4 So Q ( p ) = ( 0 if p < 2995 8+ p 64 - 4 2 . 4 (3000 - p ) 2 2 . 4 if p 2995 Part f) In the long run there is free entry so prices will be pushed down to ATC . If you charge less you make negative profits, if you charge higher no one buys from you. Thus supply is horizontal. i.e a horizontal line that passes through the intercept of MC and ATC, when firms are making zero profit.
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