Profit Calculation B78827
1. **Problem Statement:**
We are given a perfectly competitive firm producing terrible towels with the following curves: Average Total Cost (ATC), Marginal Cost (MC), Average Variable Cost (AVC), and Marginal Revenue (MR) which equals the market price $300$. We need to find the firm's total revenue, total cost, and profit.
2. **Key Information:**
- Price (P) = Marginal Revenue (MR) = $300$
- Quantity where MR=MC (profit-maximizing output) = 205 units
- Quantity where MR=ATC = 260 units
- Quantity where MR=AVC = 336 units
3. **Formulas:**
- Total Revenue (TR) = Price $\times$ Quantity
- Total Cost (TC) = Average Total Cost $\times$ Quantity
- Profit = Total Revenue $-$ Total Cost
4. **Step 1: Find Total Revenue**
At profit-maximizing output, quantity $Q = 205$ units and price $P = 300$.
$$ TR = P \times Q = 300 \times 205 = 61500 $$
5. **Step 2: Find Total Cost**
At $Q=205$, the ATC is the price at the intersection of MR and MC, which is below the ATC at $Q=260$. Since MR=ATC at $Q=260$ and price is $300$, the ATC at $Q=260$ is $300$. The ATC at $Q=205$ is higher than the MC at $Q=205$ but less than $300$ (since ATC is U-shaped and above MC). Given the graph points, we approximate ATC at $Q=205$ as about $275$ (between $225$ and $300$).
Thus,
$$ TC = ATC \times Q = 275 \times 205 = 56375 $$
6. **Step 3: Calculate Profit**
$$ \text{Profit} = TR - TC = 61500 - 56375 = 5125 $$
7. **Interpretation:**
The firm makes a positive profit of 5125 by producing 205 units at price 300.