Question

Part B: Problem Set - Vertical FDI (65 points total): Consider two firms. The first firm is based in Slovenia and produces ball bearings (upstream firm). The cost of producing ball bearings is 6 per unit. The second firm is based in Greece. This firm produces machines (downstream firm). To produce one machine, the Greek firm must buy 2 ball bearings (ignore shipping costs between Slovenia and Greece). In addition, for each machine it makes it has a production cost of 4 per machine. Machines are then sold according to the demand curve: P = 240 - 20 where P is the price of a machine and Q is the total number of machines sold. For the next four questions, assume that both firms are monopolists. 1. (5 points) Write down the profit function for the Greek firm, knowing that it imports ball bearings from the Slovenian supplier (Hint: Given the use of 2 ball bearings per machine, what is the total cost paid for ball bearings to produce one machine?) 2. (5 points) Taking the price of ball bearings as given, solve for the optimal quantity of machines produced and sold by the Greek producer. 3. (7 points) Write down the profit function for the Slovenian ball bearings supplier. Substitute for the quantity demanded using the demand coming from the Greek machine producer. (Hint: recall that the demand for ball bearings is 2 times the quantity of machines produced)

Answer 1

t. It is given that upstream firm producing ball bearings at a cost of 6 per unit meg=6 price of ball beaning = P3 (say) Downstream firm producing machine. at a cost of 4 por machine i.e. mcma 4. The demand come for machine: P=240-28. for Creek firma function to The protit 2 ball bearings a = R . Tolal Revenue - To loul cost. Tolow cost = (per unit cost of machine produces) x quarting of machi (4+2P) 8. as the firm faces a monginou eos at price PB for each machine. . Thaa PB-(4+2 Pg) & Ta (240-28) 8 - (4+2Pg) 8.1 2. optimal quantity of machine produced gta =0 58 240-49-(4+2 Pb) = 0. » 48= 240-(4+2 Pg) => 3 4 - (ons-). [p. To

3. protit function of Slovenian firm. Ts = Po. BB - 6 BB. how from (2) 48= 236 - 2Pg. Po = 236-40 produced (a). X = Now for coun unit of machine 2 units of ball beaning in produced. (B). 822BB. .. PB = 236-4 (283) - 118-4BB. - Lor), : tisa (118-4 B6) BB-GBB. much hason, it charge ton 4. dy equilibrium price of ball bearings - how equilibrium quantity STS - 118-88B -6 20. 380 302 3:14 Pg = 118-(4+14) = 62. price of bau beaning = 62/unit. equilibrium 236-2x62 on PB 262. by from (2) Q = 236 8=28. for machine: p=240-2x28 2184 Turise demond henction machine - 184/unit. i equilibrium price of

o the quontity of machine produced and sold = 28. unit. [as 8 228]. do the quantity of ball beanings produced, = 14 unit [as qa 14]. It is concutated in port 4.00]. e. protits of Slovenian firma To a P. BISH PBBB - 6QB. = (62x14) -(6x 14) 2 (62-6) 14 = 784 unit. f. profits of Greek firm - Tia = PQ-(4+2Pg) s. = (184+28) - (4+ 2x 62) 28. 2 1568 unit.