Considering the actors (i.e., two shipping lines and the port authorities) and the predetermined cost functions described below (i.e., transportation costs and port fees), and determine the equilibrium outcome (price, quantity, and profit) of the game. Let q; for i= 1 and 2 denote the number of containers transported by shipping line i. Assume a standard inverse demand function for a container of the form P=20 000 - (9₁ +9₂) , and a total transportation cost function, excluding fixed costs, of the form
Considering the actors (i.e., two shipping lines and the port authorities) and the predetermined cost functions described below (i.e., transportation costs and port fees), and determine the equilibrium outcome (price, quantity, and profit) of the game. Let q; for i= 1 and 2 denote the number of containers transported by shipping line i. Assume a standard inverse demand function for a container of the form P=20 000 - (9₁ +9₂) , and a total transportation cost function, excluding fixed costs, of the form
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Someone please clear my doubt.
I have posted question and got answer,i attached the ques and ans(refer image).
I can't understand how q1=19800 and q2=0 in equilibrium when the two actors have the same cost and revenue functions and they act simultaneously in a one-shot game. Intuitively one would guess that a cournot equillibrium would occur when q1=q2. Am I wrong i assuming that there can be no "player business that chooses to produce first" in a one-shot simultaneous game? What am i not understanding?
Transcribed Image Text:Considering the actors (i.e., two shipping lines and the port authorities) and the predetermined cost functions
described below (i.e., transportation costs and port fees), and determine the equilibrium outcome (price,
quantity, and profit) of the game. Let q, for i = 1 and 2 denote the number of containers transported by
shipping line i. Assume a standard inverse demand function for a container of the form
P= 20 000 - (q1 + q2)
, and a total transportation cost function, excluding fixed costs, of the form
TC = 200q; + (d'/2)*q,?
for i= 1,2, and t-low, high, representing low and high diseconomies of scale, i.e. dlow < dhigh, When both
shipping lines choose the port of Gothenburg, which is characterized by low diseconomies of scale, each
vessel incurs a lump sum of €1200 in port fees. In the case when both vessels choose the port of Helsingborg,
which is characterized by high diseconomies of scale, each vessel incurs €1000 in port fees. Lastly, when the
shipping lines choose different port authorities, each vessel incurs €1500 in fees. Consider that competition
takes a Cournot form and determines the equilibrium of this one-shot simultaneous game.
Transcribed Image Text:Step 1
P= 20 000 - (4, + q2)
Total Revenueli) =P*qi
TC = 200q; + (d/2)*q?
MC(i) = d(TC)/d(qi) = 200 + dt*gi
Marginal Revenue function for firm 1= d(TR(1)/dq1
= 20000 - 2q1 - q2
Marginal Revenue function for firm 2 = d(TR(2) / dq2
= 20000 - 2q2 - q1
Step 2
Now,
when both choose same port (G) (dt low)
MC(i) = 200 + 1200qi
Equilibrium Condition for best response function of firm 1: MR(1) = MC(1)
20000 - 2q1 - q2 = 200 + 1200q1
19800 – q2
q1 =
1202
( Best response function of firm 1)
Similarly ,
Equilibrium Condition for best response function of firm 2: MR(2) = MC(2)
20000 - 2q2 - q1 = 200 + 1200q2
19800 - ql
1202
( Best response function of firm 2)
q2 =
Taking value of this q2 putting in the best response function of firm 1:
19800 -42
19800 -
q1 =
1202
q1* = 19800
Putting this value into best response function of firm 2:
We get, q2* = 0
Therefore, q1* + q2* = 19800
Putting in demand function:
P= 20000 - 19800 = 200
Above game of Cournot- Duopoly in which both the players simultaneously optimize their output with respect
to other, shows us that the player firm which chooses to produce first gets to produce whole market demand.
This is due to the fact that both firms face same marginal cost function and also the demand function.
Hence whatsoever be the fees of port whether (1200, 1000 or 1500) result will be same. The firm going
first will produce for whole market demand.
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