Question

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Question 5 (13 points) (Fishermen Question) Two fishermen (balikci) went to a lake to catch carp (sazan) on a day. Let there be just one type of carp in the lake and assume that crap fishing is costless. Suppose that the second fisherman has better fishing skills and equipment than the first fisherman. In that regard, for each hour spend on the lake, the second fisherman catches 20 fish whereas the first fisherman catches 10 fish. These fishermen simultaneously decide how many hours to spend in the lake in the early morning. In the evening they meet at a common marketplace and the demand for their crap arises. Let the market de- mand for crap arises as p 100- 1 (t)-2(t2), where q(t) is the total quantity of carp caught by the fisherman i in t hours. What is the type of competition in this market and what are the fishermen's equilibrium hours to spend in the lake? A) Bertrand competition, equilibrium hours (t, t) (0, 10) 3 3 B) Cournot competition, equilibrium hours (t, t)() 3 3 C) Stackelberg quantity competition, equilibrium hours (t, t)() D) Bertrand competition, equilibrium hours (t, t) = (200 100 3 3 E) Cournot competition, equilibrium hours (t, t2) (00 100) 3 3

Answer 1

lot, 20tz a a = no a = 10 P=100-oct.) - aalta) (Profit function of fishing in 1) mi - floo-o, (t) -a, Uts) ][ 9.000] 7, = [10o - foto - Degotz] [foto] R = Rooot, -poot - 200t tz Differentiate with respect to ti იიიიიი

în - Hooot, - yoot - 200t,tz Differentiate with respect to ti = 1000 - poot, - 2oot so dit dt, t = 2000 - 2ootz 900 t = 5t

(prof it Function of Fisherman 2) T = pou no T₂ = [10o - hot, - 20t₂] [2002] 2 = 22000 t, - 200t, t₂ - Yoot? 2 - 2000 - 200t, -foot, a t = 2000-200t, et

Po Solving o ona ☺ to = lo- ta to-to (5 ) utz = lorst to ut, -z = 5 3t = 5

9M win ६ 9- s = - 0\ = 7h h 7 3 (4-5) -

It will be a cournot compeitition as fishermen are compeiting for quantities and that happens in cournot compeitition.

ANSWER - B) (10/3,5/3)