Final answer:
In a market with demand q = 10 - p and capacities k1 = 1 and k2 = 6, Firm 1 maximizes its profit by setting p1 at $9, leading to a profit of $8. Firm 2 can set p2 just below Firm 1's price to capture more market share and will have a profit of $47.94, assuming they set the price at $8.99.
Step-by-step explanation:
To determine the profits of firms in this two-stage game where they first choose capacities and then compete on prices, we need to analyze the second stage given the capacities k1 = 1 and k2 = 6. The market demand is q = 10 - p, where p represents the price. As there are no additional production costs in the second period, cost is only related to capacity, which is constant and equal to $1 per unit.
In the price competition stage, Firm 1 and Firm 2 will choose prices p1 and p2 respectively, and sell quantities q1 and q2. Since the capacities are constraints, q1 cannot exceed 1 and q2 cannot exceed 6. We presume the market will bear the lower of the two prices since the firms are selling a homogeneous product. If both firms set the price above $9, neither can sell because market demand is zero. Firm 1, with a maximum capacity of 1, has limited influence and will likely set p1 to yield one unit of sales, thus maximizing its profit at p1 = 9. Firm 2 can undercut this price slightly to capture the entire market up to its capacity of 6.
Firm 1's profit will be (Price - Average cost) * Quantity, which is (9-1)*1 = $8. Firm 2's profit, by setting a price just below Firm 1's, say at $8.99, would sell 6 units and its profit would be (8.99-1)*6 = $47.94.