This class has 26 students.

• Assume each student is a firm in the market for widgets and each firm chooses output = q_i (where "i" is a number indicating the individual firm).
• The price function for the market for widgets is P = 2000 - Q, where Q=q₁+q₂+...+q₂₆ (in other words, the sum of all of the output of all of the firms).
• Every firm has the same cost of production: $1 per widget = MC, with no fixed costs.
• This means that each firm has a profit equation of _i= (P-MC)*q_i

What is the profit maximizing choice of output for every firm? q_i = ?

(Hints: it is not possible to produce a fraction of a unit, and no firm will produce beyond the point where their marginal cost is equal to their marginal revenue. Also, you can solve this with algebra or with calculus, but every firm has the same solution).

What is the resulting Market Price? P = ?

What will the profit (_i) be for each firm if they all pursue their profit maximizing decision based on the previous math? _i = ?