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(Solved): Session 4 Problem Set Versioning Paper From Perloff, Ch. 13, pp. 475-478, #1.5, 1.6, 1.12, 2.7 Melti ...
Session 4 Problem Set
Versioning Paper
From Perloff, Ch. 13, pp. 475-478, #1.5, 1.6, 1.12, 2.7
Melting Pie - 4 period game, 5 period game
Read Perloff, Chapter 12
Extra Credit-Profit Maximization Revisited
Profit Maximization Revisited
Suppose 2 firms sell similar products in the same market. We call this a duopoly market.
The demand for firm's x and Y are given respectively
Q_(x)=44-2P_(x)+P_(y) and
Q_(y)=44-2P_(y)+P_(x)
Let's assume a constant marginal and average cost of 8 . That means that profit per unit is given
by
(\Pi _(x))/(Q_(x))=P_(x)-8 and
(\Pi _(y))/(Q_(y))=P_(y)-8 so
\Pi _(x)=(P_(x)-8)Q_(x) and
\Pi _(y)=(P_(y)-8)Q_(y),
For example
\Pi _(x)=(P_(x)-8)[44-2P_(x)+P_(y)]
Solve for the P_(x) and P_(y) which maximizes profit for firm's x and Y.
Hint: The price for X will be a function of the price for Y and the price for Y will be a function
of the price for X .
Putting P_(y) on the vertical axis and P_(x) on the horizontal axis, graph the two functions you found in
(1) on the same graph.