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1、Economics 207Intermediate MicroeconomicsSpring 2007Dr. loonie L. StoneHomework 51. Consider a perfectly-competitive, constant-cost industry.Demand in this industry is given by:Qd = 2000-20PThere are an unlimited number of identical firms with the following cost curve:TC = q2 + 20q + 900MC = 2q + 20a
2、. Find the long-run equilibrium price, quantity, and number of firms.First, find ATC by dividing TC hy Q.ATC = q + 20+ 900/qTo find the breakeven point, set MC=ATC and solve for quantity.q = 30： substitute 30 info either MC or ATC to gel the long-run price. P=$80.Thus the long-run price in this indu
3、stry is $80, and LRS is a horizontal line with a vertical intercept of $80.To find the long-run industry quantity, substitute P = $80 into the demand curve. Q = 400. Each firm will produce 30 units at a price of $80. so the number offinns is 400/30 = 13.333. Since you can 7 have a third of a firm, r
4、ound the number of firms to the nearest whole number (13).To find the short-run supply curve of the industry, first rewrite the MC curve, with P instead of MC (you can do this because the MC curve is the short-run supply curve of the firm).MC = 2q + 20P = 2q + 20Now rearrange so that q is on the lef
5、t hand side.q = -10+t/2PThere are 13 firms, so sum the quantities from 1 to 13 (or in other words, multiply the right hand side by 13). Q = -130 + 13/2 P, or P = 20 + 2/13 Q This is the INDUSTRY short-run supply curve.b. Find the equation of the short-run supply curve based on the number of firms in
6、 long-mn equilibrium. (Round number of firms to the nearest whole number.)To find the short-run supply curve of the industry, first rewrite the MC curve, with P instead of MC (you can do this because the MC curve is the short-run supply curve of the firm).MC = 2q + 20P = 2q + 20Now rearrange so that
7、 q is on the left hand side.q = -IO + l/2PThere are 13 firms, so sum the quantities from I to 13 (or in other words, multiply the right hand side by 13). Q = -I3O+ 13/2 P, or P = 20 + 2/13 Q This is the INDUSTRY short-run supply curve.c. Now suppose that demand decreases to Q = 1800 - 20P. Carefully
8、 show what will happen in (he short run and long run. and calculate the short-run and long-run prices and quantities and number of firms, and EXPLAIN what will happen in the short and long run.To find what happens in the short run, set the NEW demand curve equal to the short-run supply curve that yo
9、u found in part (b). This is the immediate impact of the fall in demand, before firms have time to enter or exit.-130+ 13/2P= 1800-20 P1930 = 53/2 PP = $72.83; Q =343.60 (or 344)There are 13 firms, so each firm produces about 26 units, and loses money. You can tell this graphically, since P is less
10、than the breakeven price, or you can calculate the loss.Thus, given enough time, some firms will exit. At the long-run breakeven price of $80, quanlily is now 200. Since the breakeven quantity is still 30, there will now be 200/30 = 6 2/3 (round to 7) firms. The new short-run supply curve, with 7 fi
11、rms in the market, is Q = -70 + 7/2 P.(NOTE: I changed this demand curve from what I had originally posted after receiving a very good email question. If you worked this problem with that demand curve, thats fine, too, but your long- run answer must make sense with what would occur in that case.)If
12、you worked the problem this way, note that the vertical intercept of the demand curve (Q = 1500 - 20P) is $75, which is below the breakeven price. Thus the price will drop further in the short run (to $63, / think, if you calculate it), and in the long run, ALL firms will exit this industry since th
13、ey cannot break even at any price on the demand curve.d. Carefully graph your results. You should have a graph for the industry, a graph for the firm, and you should show all short and long-run points (hat you found in a, b. and c.Graphs will be posted in a separate file shortly (probably Tuesday morning).
