Question

Two firms (Natural Salt and Healthy Salt) compete in the market for Himalayan table salt. Consumers see the salt produced by both firms as perfect substitutes. In this market, each firm chooses what output to produce and price is determined by aggregate output. Market demand is given by ? = 450 − 2?, where ? is kgs and ? is €/kg. The initial marginal cost of Natural Salt is 50€/kg. The respective for Healthy Salt is 40€/kg. A process innovation in the production technology of Himalayan table salt would reduce the Natural Salt’s marginal cost to 44 and Healthy Salt’s marginal cost to 34.

(a) Consider that only one of the two firms can introduce the aforementioned process innovation in its production technology, while its rival firm still produces with its initial marginal cost. How much would each firm be willing to pay so as to introduce the aforementioned process innovation in its production technology?

(b) Consider that each firm has the option to pay 1,000 euros so as to introduce the aforementioned process innovation in its production technology. Given each firm’s decision, on whether to introduce the innovation or not, firms compete in the market by choosing simultaneously their level of output. If you were the Natural Salt’s manager, would you suggest the introduction of the innovation or not? What would you suggest if you were the Healthy Salt’s manager? [Hint: Construct a payoff matrix.]

c) Assume that Natural Salt and Healthy Salt decide on the following: Healthy Salt pays 1,000 euros and introduces the process innovation. Then, the two firms merge and produce with marginal cost equal to 34. Healthy Salt keeps 500 euros of the post-merger firm’s profits (half of the process innovation’s cost) and the remaining profits are equally shared to the merger participating firms. Do both firms have incentives for such a merger, as compared to the equilibrium in (b)?

(d) How does the merger change consumer’s surplus and social welfare, compared to the respective ones in (b)?

[Marking scheme: economic intuition 10%, use of appropriate formulae 40%, correct calculations 30%, overall presentation 20%]

It has to do with oligopolistic competition.

Answer 1

a) Q is the aggregate output demanded. Let Qi and Q2 be the output produced by the two firms. Solve for the inverse demand function as follows: Q+Q2 = 450 - 2P P=225 -0.50 -0.592 Suppose natural salt innovates, then the profit functions are as follows: Ty =(225 – 0.50 -0.5Q)-44% Aty = 2250,-0.50 -0.50,- 44Q, TH =(225– 0.50 -0.59,,-400, Ty = 22592-0.5992-0.593 - 40Q2 Solve for the profit maximizing quantity and price as follows: N = 225-Q-0.592 - 44 89. 0= 225-97-0.59,-44 +0.5Q, =181 Q2 hot n = 225 -0.50 -0; -40 0 = 225 -0.59,-92-40 22 +0.50 =185

Next, solve for (1) and (2) as follows: Q +0.5(185 – 0.52)=181 +92.5 -0.25Q. = 181 0.759 = 88.5 Q =118 Q2 = 185 -0.5(118) 2 =126 P=225 -0.5(118) -0.5(126) P=103 Therefore, when Natural salt innovates then price is $103, quantity produced by natural salt is 118, quantity produced by healthy salt is 126, and total quantity produced is 244. Suppose healthy salt innovates, then the profit functions are as follows: Tx = (225 -0.59-0.592)9-509. 7 = 2250 -0.50 -0.5QQ, - 500 TH =(225 – 0.50 -0.5Q)Q - 349, TH = 2250,-0.5QQ, -0.50-34Q, Solve for the profit maximizing quantity and price as follows:

8Q ON = 225 - 0,-0.59, -50 0 = 225-97-0.592 - 50 9+0.592 =175 H = 225 -0.59-92-34 802 0 = 225–0.59-92-34 02+0.50 =191 Next, solve for (3) and (4) as follows:

Q1 +0.5(191 -0.59) = 175 +95.5-0.259 = 175 0.759, = 79.5 Q =106 Q =191 -0.5(106) 22 =138 P=225 - 0.5(106)-0.5(138) P=103 Therefore, when Natural salt innovates then price is $103, quantity produced by natural salt is 106, quantity produced by healthy salt is 138, and total quantity produced is 244. Now, suppose none of them introduces the new technology, then: =(225 – 0.50 -0.5Q), -500 Ty = 225g-0.50 -0.5992 – 509, TH =(225 – 0.50 -0.59,00,-400, TH = 225Q, -0.5QQ, -0.50 - 400, Solve for the profit maximizing quantity and price as follows: = 225-0-0.592-50 80, 0= 225-Q -0.592-50 9 +0.5Q2 = 175 ...(5)

"H = 225 -0.5Q.--40 SQ2 0 = 225–0.59,-92-40 IQ, +0.5Q = 185 ...(6) Next, solve for (5) and (6) as follows: Q1 +0.5(185–0.59)=175 +92.5 -0.259 = 175 0.75Q = 82.5 0 =110 Q2 = 185 -0.5(110) 0 =130 P=225 -0.5(110)-0.5(130) P=105 Now, each firm will be willing to pay equal to the amount of the increase in profits. Calculate the same as follows: Natural Salt's willingness to pay =Profit with technology - Profit without technology =[(103 – 44)x118]-[(103 – 50)x106] = $6,962 - $5,618 = $1,344

Healthy Salt's willingness to pay =Profit with technology - Profit without technology =[(103 – 34)x138]-[(103 – 40)x126] = $9,522-$7,938 = $1,584 Therefore, Natural salt's willingness to pay for the technology is $1,344 and Healthy salt's willingness to pay for the technology is $1,584 Suppose both of them introduce the new technology, then using (1) and (4): Q+0.592 = 181 Q2 +0.59 = 191 Solve for the two equations:

Q1 +0.5(191-0.59) = 181 Q +95.5-0.259 = 181 0.75Q = 85.5 9 =114 Q2 = 191 -0.5(114) 92 =134 Q=248 P= 225 -0.5(248) P=$101 Now, find out the change in revenue as follows: (i)Natural Salt's Payoff: (101x114)-(103 x106)-1000 = -404 Healthy Salt's Payoff: (101x134)-(103 x126)-1000 = -444 (ii) Natural Salt's Payoff: (103x118)-(105x110)-1000 = -396 Healthy Salt's Payoff: (126x103)-(134x101) = -556 (iii)Natural Salt's Payoff: (103x106)–(101x114)= -596 Healthy Salt's Payoff: (103x138)-(130x105)-1000 = - 444 (iv)Natural Salt's Payoff: (105x110)-(103x118)= -604 Healthy Salt's Payoff: (105x130)-(138x103) = -564 Next, construct the payoff matrix as follows: Natural Salt Healthy Salt Introduce -404,-444 -596, -444 Introduce Doesn't Introduce Doesn't Introduce -396, -556 -604, -564

Therefore, both the firms should introduce the technology. c) The combined profit after the merger is as follows: 1 = (225-0.59)9-349 A = 2259-0.502 – 349 St = 225 - Q-34 80 0= 225-Q-34 Q=191 P= 225 – 0.5(191) P= $129.5 Profit = 191x129.5 – 34x191 Profit = $18,240.5 Now, the share of profit of each firm is: ($18,240.5-$500 Healthy Salt's profit = $500+ $9,370.25 $18, 240.5-$500 Natural Salt's profit = 2. = $8,870.25 Now, evaluate the incentives for the two firms to merge as follows:

Gain for Natural Salt = Profits after merger – Profits in part b's equilibrium =$8,870.25 – $6,498 = $2,372.25 Gain for Healthy Salt = Profits after merger - Profits in part b's equilibrium - $1,000 =$9,370.25 - $8,978-$1,000 =-$607.75 Therefore, only Natural Salt has the incentive to merge as it is receiving positive gain.

Price/Cost $225 $129.5 $101 $44 $34 D - Quantity 191 248 362 382 Calculate the consumer surplus in part b's equilibrium as follows: Consumer surplus in part b’s equilibrium =-x(225–101)x 248 = $15,376 Calculate the consumer surplus in case of merger as follows: Consumer surplus with merger - 129.5) 191 = $9,120.25 Calculate the social welfare in case of part b's equilibrium as follows:

Social welfare in part b's equilibrium = Consumer surplus + Profits - Dead weight loss = $15,376 +[114x (101 – 44) +134x(101 – 34)] -(101- 44)(362–248) + 3(101 – 34)(382– 248)] = $15,376+$15,476 – $7,738 = $23,114 Social welfare with merger = Consumer surplus + Profits - Dead weight loss = $9,120.25 +$18, 240 -34) (382-191) = $9,120.25 +$18, 240.5 – $9,120.25 = $18,240.5 Therefore, the consumer surplus as well as social welfare has decreased after the merger.