Schure tests06ans

Question 1 2 a true see eg figure 1115 b true see eg

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Question 1-2 (a) TRUE [See e.g. Figure 11.15] (b) TRUE [See e.g. Figures 11.6 + 11.7] (c) TRUE [See defn equilibriums in the SR and LR] Question 2-1 (a1) (3 marks) max Q Π ( Q ) = (60 Q ) Q 0 . 5 Q 2 275 . [Alternatively: max P Π ( P ) = P (60 P ) 0 . 5(60 P ) 2 275 . ] (a2) (3 marks) The FOC is 60 2 Q Q = 0 . This yields Q M = 20 , so that P M = 60 20 = 40 . (a3) (4 marks) See the picture. CS in yellow (light) and PS in blue (dark) (b1) (total:7 marks) STEP 1: (3 marks) You can depart from the monopolists problem, or do things directly. There are two paths you can follow: (1) formulate the monopolists problem as to maximize pro fi ts by choosing prices optimally, (2) formulate the monopolists problem as to maximize pro fi ts by choosing quantities optimally. The last is the easiest. Reward students that write up the monopolist’s problem correctly by 3 points because they have got a very good start. If students skip this step but arrive at the next, that is fi ne too. STEP 2. (2 marks) Going the quantity way is the easiest and you arrive at the following two conditions: MR A ( Q A ) = MC ( Q ) MR B ( Q B ) = MC ( Q ) where Q = Q A + Q B . In this case the equations are: 55 2 Q A = Q A + Q B 1

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Figure 1: The consumer and producer surplus 35 Q B = Q A + Q B STEP 3 (3 marks) Figure out the total quantity that the monopolist produces. That is solve the two equations. For example substitute eqn (2) in (1) to get 55 3(35 2 Q B ) Q B = 0. This delivers Q B = 10 . Substitute back in eqn (2) to see that Q A = 15 . (b2) (3 marks). The optimal prices with price discrimination are P A = 55 15 = 40 and P B = 35 1 2 10 = 30 . The cost or arbitrage must therefore exceed \$10 per unit to make this form of price discrimination work. Question 2-2 (a) (4 marks) It means two changes (1) getting rid of the price guarantee of P = 20 per bushel (That is, do not interbene in the market by o ff ering P = 20 . Market forces will determine the price); (2). Allow farmers to start growing wheat (i.e. allow entry). (b) (6 marks) with a price of P = 20 individual fi rms o ff er q i such that P = MC ( q i ) = q i 4 . Since the supply of an individual fi rm is given by P = q i 4 or q i = P +4 = 24 the market supply is given by Q = 10 , 000 P + 40 , 000 . With P = 20 we get Q = 240 , 000 . Two remarks [not needed in your answer] Another way: individual supply determined by P = q i 4 so q i = 24 if P = 20 . Hence with 10,000 fi rms supply is 10 , 000 24 = 240 , 000 2
We know that the price must be higher than the minimum level of the average variable cost for fi rms to be willing to produce in the SR. The AVC is given by V C ( q i ) /q i = 0 . 5 q i 4 . The minimum level of the AVC is hence 4 (BTW, what would this mean?). Thus P = q i 4 applies for all prices P 0 because even at P = 0 the fi rm would like to stay in business in the short run. (c) (4 marks) [In this question you need to derive the market supply curve if you have not yet in (b)]. Immediately after the coop student’s proposal gets implemented supply and demand determine the price. Supply is given by Q = 10 , 000 P + 40 , 000 , demand is given by Q = 10 , 000 P + 400 , 000 . Hence the equilibrium price is given by 10 , 000 P + 40 , 000 = 10 , 000 P + 400 , 000 20 , 000 P = 360 , 000 P = 18 . [Each fi
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