Q7. Competition, oligopoly, monopoly, Nash equilibrium, subgame-perfect Nash equilibrium, and backward induction. Assume that there are N firms that sell mobile phones, where N is a positive integer, and assume that when N> 1 the firms' products are exactly alike (when N = 1 there is just one seller). N is thus a fixed number, and everyone knows which that number is (N is common knowledge). Potential buyers are homogenous in their valuation for mobile phones and each potential buyer consumes at most 1 mobile phone. Suppose that there are 900 potential buyers and each has a willingness to pay $700 for a mobile phone. = Assume that each firm's total production costs TC(q) are given by the function TC(q) = 200000 + 300q when q > 0, and TC(q) 0 when q = 0, where q is the quant pro- duced by the firm. Assume that firms choose prices and that the firms choose their prices simultaneously and non-cooperatively. Determine consumer surplus in equilibrium when N = 1. Write your answer (consumer surplus) here and explain below. b) Determine consumer surplus in equilibrium when N > 1. Write your answer (consumer surplus) here and explain below. Assume now that firms make their decisions sequentially (i.e. first firm 1 decides, then firm 2 decides, then firm 3 decides, then firm N decides). Assume all firms know the order in which firms make the decisions. Determine consumer surplus in equilibrium when N = 2. Write your answer (consumer surplus) here and explain below. ****
Q7. Competition, oligopoly, monopoly, Nash equilibrium, subgame-perfect Nash equilibrium, and backward induction. Assume that there are N firms that sell mobile phones, where N is a positive integer, and assume that when N> 1 the firms' products are exactly alike (when N = 1 there is just one seller). N is thus a fixed number, and everyone knows which that number is (N is common knowledge). Potential buyers are homogenous in their valuation for mobile phones and each potential buyer consumes at most 1 mobile phone. Suppose that there are 900 potential buyers and each has a willingness to pay $700 for a mobile phone. = Assume that each firm's total production costs TC(q) are given by the function TC(q) = 200000 + 300q when q > 0, and TC(q) 0 when q = 0, where q is the quant pro- duced by the firm. Assume that firms choose prices and that the firms choose their prices simultaneously and non-cooperatively. Determine consumer surplus in equilibrium when N = 1. Write your answer (consumer surplus) here and explain below. b) Determine consumer surplus in equilibrium when N > 1. Write your answer (consumer surplus) here and explain below. Assume now that firms make their decisions sequentially (i.e. first firm 1 decides, then firm 2 decides, then firm 3 decides, then firm N decides). Assume all firms know the order in which firms make the decisions. Determine consumer surplus in equilibrium when N = 2. Write your answer (consumer surplus) here and explain below. ****
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Q7.
Competition, oligopoly, monopoly, Nash equilibrium, subgame-perfect Nash
equilibrium, and backward induction.
●
Assume that there are N firms that sell mobile phones, where N is a positive integer, and
assume that when N> 1 the firms' products are exactly alike (when N = 1 there is just one
seller). N is thus a fixed number, and everyone knows which that number is (N is common
knowledge).
Potential buyers are homogenous in their valuation for mobile phones and each potential
buyer consumes at most 1 mobile phone. Suppose that there are 900 potential buyers and
each has a willingness to pay $700 for a mobile phone.
Assume that each firm's total production costs TC(q) are given by the function TC(q) =
200000 + 300g when q> 0, and TC(q) = 0 when q = 0, where q is the quantity pro-
duced by the firm. Assume that firms choose prices and that the firms choose their prices
simultaneously and non-cooperatively.
a)
Determine consumer surplus in equilibrium when N = 1. Write your answer
(consumer surplus) here and explain below.
11
b)
Determine consumer surplus in equilibrium when N > 1. Write your answer
(consumer surplus) here and explain below.
...y
c)
Assume now that firms make their decisions sequentially (i.e. first firm 1
decides, then firm 2 decides, then firm 3 decides, then firm N decides). Assume all
firms know the order in which firms make the decisions. Determine consumer surplus in
equilibrium when N = 2. Write your answer (consumer surplus) here
and explain
below.
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