Question

The market for a good (e.g. cars) is characterized by monopolistic competition, such that demand for each firm's product is given by: $Q = S \left[ \frac{1}{N} - r(P - \bar{P}) \right]$ where $S$ denotes the size of the market, $N$ denotes the number of firms producing, and $\bar{P}$ denotes the average price charged by firms in the market. All firms produce with the same technology, which features a constant marginal cost $c$ and a fixed cost of production $f$, such that the total cost for a firm producing $Q$ units of output is: $TC = cQ + f$ In what follows, assume that the parameter values are: $S = 10$ $r = 0.01$ $c = 1$ Furthermore, suppose that the number of firms producing is fixed, and is given by: $N = 100$ 1. What output level ($Q$) and price ($P$) does each firm choose in equilibrium when all firms maximize profits? (15 points) 2. What must the value of the fixed production cost ($f$) be such that all firms earn zero operating profits (i.e. revenue minus total production costs)? (10 points)

          The market for a good (e.g. cars) is characterized by monopolistic competition, such that demand for each firm's product is given by:
$Q = S \left[ \frac{1}{N} - r(P - \bar{P}) \right]$
where $S$ denotes the size of the market, $N$ denotes the number of firms producing, and $\bar{P}$ denotes the average price charged by firms in the market. All firms produce with the same technology, which features a constant marginal cost $c$ and a fixed cost of production $f$, such that the total cost for a firm producing $Q$ units of output is:
$TC = cQ + f$
In what follows, assume that the parameter values are:
$S = 10$
$r = 0.01$
$c = 1$
Furthermore, suppose that the number of firms producing is fixed, and is given by:
$N = 100$
1. What output level ($Q$) and price ($P$) does each firm choose in equilibrium when all firms maximize profits? (15 points)
2. What must the value of the fixed production cost ($f$) be such that all firms earn zero operating profits (i.e. revenue minus total production costs)? (10 points)

The market for a good (e.g. cars) is characterized by monopolistic competition, such that demand for each firm's product is given by:
Q = S [ (1)/(N) - r(P - P̅) ]
where S denotes the size of the market, N denotes the number of firms producing, and P̅ denotes the average price charged by firms in the market. All firms produce with the same technology, which features a constant marginal cost c and a fixed cost of production f, such that the total cost for a firm producing Q units of output is:
TC = cQ + f
In what follows, assume that the parameter values are:
S = 10
r = 0.01
c = 1
Furthermore, suppose that the number of firms producing is fixed, and is given by:
N = 100
1. What output level (Q) and price (P) does each firm choose in equilibrium when all firms maximize profits? (15 points)
2. What must the value of the fixed production cost (f) be such that all firms earn zero operating profits (i.e. revenue minus total production costs)? (10 points)

Added by Christian H.

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