In: Economics
If there are two companies making the same model of cellphones.
Assuming the demand for the cellphones produced by Company 1 is D1,
and the demand for the cellphones produced by Comp nay 2 is D2, are
described by the following two functions:
D1=200-P1-(P1-P)
D2=170-P2-(P2-P)
where P is the average price over the prices of the two companies,
i.e., P=[P1+P2]/2. Each company has the cost of C1=C2=10 for
producing one cellphone. Suppose each company can only choose one
of the three prices {40, 70, 90} for sale.
(1] Compute the profits of each company under all sale price combinations and make the payoff matrix for the two companies. [Hint: the total profits = the demand for the cellphones * the profit of one cellphone after sale. You can type the pay off table for each company as a matrix in the ansering box such that the first row and first column present strategies.]
(2] Find the Nash equilibrium of this game. What are the profits at this equilibrium? Explain your reason clearly.
(3) If the cost for Company 2 changed as C2=20, would the Nash
equilibrium change? Why?