practice1_ak.pdf - 1(a AT C(q = F=q c So AT C is decreasing...

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1. (a) ATC ( q ) = F=q + c . So ATC is decreasing for all q > 0 : Thus, the average cost is not minimized for any °nite value of q . (b) First, °nd q that equates MR and MC : MR ( q ) = dTR ( q ) dq = ° 2 q + 100 MC ( q ) = dTC ( q ) dq = 10 Thus q ° = 45 and p ° = 55 . The consumer surplus is (100 ° 55) ± 45 ± 1 2 = 1012 : 5 : The total surplus in this case is CS + PS = 1012 : 5 + ( p m ° MC ( q m )) ± q m = 3037 : 5 : The total surplus in the case of perfect competition is (100 ° 10) ± 90 ± 1 2 = 4050 : Thus, the di/erence is 1012 : 5 , which equals to the dead-weight loss. (c) AC ( q ) = 10 + 800 =q: Now we are considering a monopolist, so q = Q: Using the demand function, p = 100 ° q = AC ( q ) : Thus, we have q = 80 (mathematically q = 10 is also a solution to this equation, but let±s focus on the larger q as we discussed in class). The total surplus is CS + PS = 80 ± 80 ± 1 2 +0 = 3200 : The total surplus in the case of perfect competition is 90 ± 90 ± 1 2 ° 800 = 3250 : The dead-weight loss is 50 . (d) The marginal revenue for each market is MR 1 ( q 1 ) = 50 ° q 1 and MR 2 ( q 2 ) = 100 ° 4 q 2 ; respectively.
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