1.(Assume that a firm M (the manufacturer) sells an input (a lawn mower) to firm R (the retailer). Now R sells the lawn mower to the public, incurring a constant cost of $10 per lawn mower for its services.Fixedproportions production holds for R.Let X therefore represent the number of lawn mowers.If both M and R are monopolists andP_Lis the lawn mower price charged to the public with demand

X=100.5P_L

Answer the following questions:

a)Find the derived demand for lawn mowers facing M.Hint: Find the marginal revenue equal marginal cost condition for R, where R's marginal cost is the sum of the $15 and the priceP_Xthat it must pay M per lawn mower.Solving for X gives the derived demand.

b)If M's marginal cost function is 40 find the equilibrium prices and quantities

P P_L,_xandX

c)Assume now that M and R form a single vertically integrated firm, M-R. Find the equilibrium values ofP_Land X and the profit of M-R.

d)Compare the unintegrated case in part b with the integrated case in part c.Is it true that both the firms and the public would prefer the case in part c? Explain.