请教一个尼科尔森的习题，敬请指教：）
题目是：
The perfectly competitive videotape copying industry is composed of many firms that cancopy five tapes per day at an average cost of $10 per tape. Each firm must also pay a royaltyto film studios, and the per-film royalty rate (r) is an increasing function of total industry out-put (Q) given by r=.002Q

Demand is given by Q=1050-50P

a.Assuming the industry is in long-run equilibrium, what will be the equilibrium price andquantity of copied tapes? How many tape firms will there be? What will the per-film roy-alty rate be?

b.Suppose demand for copied tapes increases to Q=1600-50P
Now, what is the long-run equilibrium price and quantity for copied tapes? How manytape firms are there? What is the per-film royalty rate?

c.Graph these long-run equilibria in the tape market and calculate the increase in pro-ducer surplus between the situations described in parts (a) and (b).

d.Show that the increase in producer surplus is precisely equal to the increase in royalties
paid as Qexpands incrementally from its level in part (b) to its level in part (c).


答案是这样，问题是不知道第四题是怎么解的？为什么第四题是个租值变化呢？

11.3     a.   The long-run equilibrium price is 10 + r = 10 + .002Q.

                  So,Q = 1050 – 50(10 + .002Q) = 550 + .1Q   so

             Q= 500, P = 11, r = 1.

            b.   Now Q= 1600 – 50(10 + .002Q) = 1100 + .1Q

             Q = 1000, P = 12, r = 2.

            c.   Change in PS= 1(500) + .5(1)(500) = 750.

            d.   Change in rents = 1(500) + .5(1)(500) =750.  The areas are equal.