Question

Two firms have their operations in the same building. One firm conducts tests of firecrackers for manufacturers of fireworks. Assume firecracker tests F are sold in a competitive market at constant price $50. The testing firm's cost is TC(F) = 5F2 The second firm is a relaxing day spa. They produce spa services that sell at a constant market price of $40. The spa's cost of production is TC(S) = S2 - 10S + 10F. The quantity of firecrackers produced enters the cost function of the spa, because they have to burn extra sensory candles to create a relaxing environment when there are loud noises coming from the firecracker test facility. To illustrate Coasian logic, we need to first establish what the firms will do in the absence of negotiation and the absence of policy. 15. Suppose there is no policy and no negotiation between the parties. What is the quantity of F produced, denote this as Fm? (1 point) 16. What is the quantity of S produced, denote this as Sm? (1 point) To show how policy and negotiation can both move the market to the optimal allocation, we need to find the optimal allocation. (Hint: to find the social optimum, you can maximize total profits across both firms.) 17. What is the socially optimal (efficient) quantity of F, denote this as F*? (1 point) 18. What is the socially optimal efficient) quantity of S, denote this as S? (1 point)

Answer 1

testing firm's cost, TC; = 5f price of testing firm's test, pf = $50 spa's cost, TC5 = 5? – 10s + 10f price of spa's services, p = $40

Here testing firm's output affects the total cost of the spa. Increase in testing firm's output increases the total cost of spa and thereby decreasing the spa's profits.

Part (15) if the testing firm does not takes into accoun the effect of its activities on the spa

profits of testing firm, az = TR– TC; T = Pf* f - 5f T = 50f - 51 differentiating with respect to f and equating to 0 to maximize profit dif = 50 - 10f = 0 df 50 To = 5 = -10 < 0

i in absence of policy negotiation between the parties output of testing firm, f = 5

Part (16)

profits of spa, 7, = TR, - TC Ts = ps*S-5+ 10s - 10f T13 = 40s - $? + 10s – 10 * 5 Tis = 50s – 52 - 50 taking first derivative with respect to s and equating to 0 to maximize profit = 50 – 2s = 0 s=* = 25 ds2=-2 <0

i in absence of policy negotiation between the parties output of spa, s = 25

Part (17) to find socially optimum output for both entities, we maxmize the joint profits

T = 1; +T = 50f -5f2 + 40s – s2 +10s – 10f 7 = 40f – 512 + 50s – 82 taking first derivative with respect to f and equating to 0 to maximize profits = 40 - 10f = 0 af f = 1 = 4 40 af2 = -10 < 0

:: socially optimum output of testing firm f* = 4 units

Part (18)

T = Tg+ = 50f -5f2 + 40s – s2 +10s – 10f 7 = 40f – 512 + 50s – 82 taking first derivative with respect to s and equating to 0 to maximize profits = 50 - 2s=0 as 50 s= = 25 22 052 = -20

:socially optimum output of spa s* = 25 units