1. **Problem Statement:** Determine Big Top's profit-maximizing price, output, and economic profit when charging a single price for all tickets. 2. **Given Data:** | Price ($) | Quantity (tickets) | Total Cost ($) | |-----------|--------------------|----------------| | 30 | 0 | 1000 | | 27 | 100 | 1900 | | 24 | 200 | 2800 | | 21 | 300 | 3700 | | 18 | 400 | 4600 | | 15 | 500 | 5500 | | 12 | 600 | 6400 | | 9 | 700 | 7300 | | 6 | 800 | 8200 | 3. **Formula for Profit:** $$\text{Profit} = \text{Total Revenue} - \text{Total Cost}$$ where $$\text{Total Revenue} = \text{Price} \times \text{Quantity}$$ 4. **Calculate Total Revenue and Profit for each quantity:** - For 0 tickets: Revenue = $30 \times 0 = 0$, Profit = $0 - 1000 = -1000$ - For 100 tickets: Revenue = $27 \times 100 = 2700$, Profit = $2700 - 1900 = 800$ - For 200 tickets: Revenue = $24 \times 200 = 4800$, Profit = $4800 - 2800 = 2000$ - For 300 tickets: Revenue = $21 \times 300 = 6300$, Profit = $6300 - 3700 = 2600$ - For 400 tickets: Revenue = $18 \times 400 = 7200$, Profit = $7200 - 4600 = 2600$ - For 500 tickets: Revenue = $15 \times 500 = 7500$, Profit = $7500 - 5500 = 2000$ - For 600 tickets: Revenue = $12 \times 600 = 7200$, Profit = $7200 - 6400 = 800$ - For 700 tickets: Revenue = $9 \times 700 = 6300$, Profit = $6300 - 7300 = -1000$ - For 800 tickets: Revenue = $6 \times 800 = 4800$, Profit = $4800 - 8200 = -3400$ 5. **Identify the maximum profit:** The maximum profit is $2600$ dollars, achieved at both 300 and 400 tickets. 6. **Choose the profit-maximizing output and price:** Between 300 and 400 tickets, the price at 300 tickets is $21$ and at 400 tickets is $18$. Both yield the same profit, but typically the firm chooses the output with higher price to maximize revenue per ticket. **Final answers:** - Profit-maximizing output: $300$ tickets - Profit-maximizing price: $21$ dollars per ticket - Economic profit: $2600$ dollars