Question

A monopoly company has a cost function TC (Q) = Q and sells its product on the Italian and Greek markets. The Greek market has a demand function DE (P) = 6 − P for P ≤ 6 and 0 elsewhere, while the Italian market has a demand function DI (P) = 8 - P for P ≤ 8 and 0 elsewhere.

(a) Calculate the single price that maximizes the firm's profits, quantity sold and profits.

(b) If the company has the opportunity to set different prices on the two markets to calculate those prices, the quantities sold and the corresponding profits.

Answer 1

Total cost TC(27= Q.; Greek demand: D (P.) = 6-p. in Italian demand : DI (P) = &-P al Market demand релсат- = p<67 D = Det De z6pts-p=14-20 (both markets ) P = 14-22]. [d=14-2P ] [let D be replaced by Q] P= 14-02 Fortal force . - boveny E= Profit (t)= Total Revenue - coste. = P Q - TT = 14-07-02; 71 = (yaca?).- ; maximizing it dT 14-20_1=0 [P= 14= 4] [fröfit = pa-Q = 46036410 J... : for [6<P <8] (only Italian market) market demand i Dz DI = D z 8-p (let D = 0) [h=8-p] (P=8-Q ] Profit= pica-a= (8-0) a antal T = 84-0²-a =74-02 maximizing profili du. 7-2 d = o . [3.5=4]. [P= 8-3.5 = 4.5] Profit a p. 6-a = 4.5(3:5) -3.5 = $12.25

DNP Since profit of o is greter than profit of ③ single price ip = $4 g luantity (a = 6] . [Profit = $18 ]. b) Ver for italian market we have solved in .. part (a) we got [p = $4.5] [6 = 35 ] (enentity) Profit = $.12-25 for Greek market a= 6-p. =) .P = 6:4 Profita pa al =(6-0) ara=60-0-0 17 = 54-.? to... maximizing ; : A T z 5-20 =0 [2.52.07 Quantity P= 6-A -- 6-2.5-3.5 [P= $3.5] price Profit= pora 313-5712-57-275) (Profit = $6.25