Question

a) Consider a merger among firms producing two complementary goods, computer (x) and memory card (Y). The consumers treat both goods as perfect complements. One computer systems is composed of one computer and two memory cards. The demand for a computer system is given as Q = a – Ps = a – Px – 2py, where Q = x = 5, a > 0. Let Px denote the price of a computer, and py denote the price of a single memory card. Assume that production is costless. Suppose that the X producer and the Y producer are independent. Solve for the Nash-Bertrand equilibrium in prices. Calculate the equilibrium prices, the quantity produced of each product, and the firms' profit levels! b) Now suppose that firm X and Y merge under a single ownership. Calculate the monopoly equilibrium prices, the quantity produced of each product, and the monopoly's profit! Is this merger welfare-improving? Compare system prices and profits of the firms before and after the merger! c)
Hi, can anyone solve the following questions a) and b) circled in red in a easier and simplied way ?. I have also posted the solution for this. Thanks

Answer 1

classmate Date Page bofit - Revenue - costs x= PxQ - 0 Px (X-Ps) (production is coolless) (Q = x gwen) [Ps - Pxtaly Px (4-Pn-2ly) 2Px - Pa ²-2kely IP) Profit to O froat we will solve fx for geen py differentiating Profit with respect to ke, and then equating d-spx I ly = 0 JPx t-2y = bx 2 Px = x - Py 2 Solving = similarly for ly Al it then Olly My = Pyly o (costs are zero (22= y) Py2Q = 2ly ( x - Pn-2y) 2aly-2fely -4 Pye 2x - 2/x -8 Py aly x-px 4 Py 2) Selling 0 & ② to px = x - get 2 tu 2 4 4 타 22 12 3 p = 4 4. P = 2/3 Scanned by TapScanner

classmate Nay, les- Pataly Date Page X 2 3 Ps= 22 Q = X-Ps (given) Q = *-28 - z Calculating Profits for seller of a & y 2 Te = n2 = x. 4 = 3 3 9 y = Py 2Q = (4/2) ( x ) = 4 merge as b) Now, from and y monopoly Now, merged profit equation is, ITS = PsQ Ps (x-Ps) & Ps-Ps² Is = Differentiating Its with respect to Ps, dits x-2ps dps Qs = x-ps = x-x/ Qs = 42 2 Prefits = Qsfs. - 0 T (42) (2/2) = x Scanned by TapScanner