Suppose there are two firms in a perfectly competitive market, Firm A and Firm B, who both produce widgets. The demand for widgets is given by the following equation:

P = 100 - 2Q

where P is the price of the widget (in dollars) and Q is the quantity of widgets produced (in units). The cost functions for the two firms are given by the following equations:

Firm A: C(Q) = 10Q + 20

Firm B: C(Q) = 5Q + 30

Both firms have a constant marginal cost of $10 per widget.

1. Find the profit-maximizing quantity of widgets for each firm.
2. Find the profit-maximizing price for each firm.
3. Find the profit for each firm at the profit-maximizing quantity and price.
4. Assume that the firms are currently producing their profit-maximizing quantities and that the market price is $70. At this price, will Firm A increase or decrease production? Why?

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