1 clipit is a paper clip manufacturer the company

Question

1. ClipIt is a paper clip manufacturer. The company enjoys a patented technology that allows it to produce paper clips faster and at a lower cost than its only rival, FastenIt.  ClipIt uses this advantage to be the first to choose its profit-maximizing output level in the market. The inverse demand function for paper clips is P = 500 - 2Q, where Q = Q_c + Q_f . ClipIt's costs are C_c(Q_c)= 2Q_c, and FastenIt's costs are C_f(Q_f)= 4Q_f.

(a) What is ClipIt's profit-maximizing output level? FastenIt's? 

(b) What is the market's equilibrium price? (c) How much profit does each firm earn?

(d) Would it be profitable for your firm to merge with FastenIt?

2. The Winston Tobacco Company feels that it is faced with the following segmented demand function for its cigarettes:

                     10 - 0.1Q  when 0 ≤ Q ≤ 20

P =

                      12 - 0.2Q  when     Q > 20

where Q is the number of cartons sold and P is the price per carton.

(a) Why is such a segmented demand function likely to exist? What type of industry structure and firm behavior is indicated by this relationship?

(b) Determine Winston's marginal revenue function. (c) Given that Winston's total cost function is

TC₁ = 80 + 2.6Q + 0.05Q²

determine Winston's profit maximizing price and output level. (Use MC₁ = 2.6 + 0.1Q.) (d) Given that Winston's total cost function increases to

TC2 = 90 + 3.4Q + 0.05Q2

what is their profit maximizing price and output level? (Use MC2 = 3.4 + 0.1Q.)