Subjects microeconomics

Profit Calculation B78827

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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.