The following table shows the total cost schedule of a competitive firm. It is given that the price of the good is Rs 10. Calculate the profit at each output level. Find the profit maximising level of output.
| Output | TC (Rs) |
|---|---|
| 0 | 5 |
| 1 | 15 |
| 2 | 22 |
| 3 | 27 |
| 4 | 31 |
| 5 | 38 |
| 6 | 49 |
| 7 | 63 |
| 8 | 81 |
| 9 | 101 |
| 10 | 123 |
The profit at each output level is calculated using the formula: Profit (π) = Total Revenue (TR) – Total Cost (TC), where TR = Price × Output.
Step 1: Calculate TR and Profit at each output level
| Output | TC (Rs) | TR = P × Q (Rs) | Profit = TR – TC (Rs) |
|---|---|---|---|
| 0 | 5 | = 0 | 0 – 5 = –5 |
| 1 | 15 | = 10 | 10 – 15 = –5 |
| 2 | 22 | = 20 | 20 – 22 = –2 |
| 3 | 27 | = 30 | 30 – 27 = 3 |
| 4 | 31 | = 40 | 40 – 31 = 9 |
| 5 | 38 | = 50 | 50 – 38 = 12 |
| 6 | 49 | = 60 | 60 – 49 = 11 |
| 7 | 63 | = 70 | 70 – 63 = 7 |
| 8 | 81 | = 80 | 80 – 81 = –1 |
| 9 | 101 | = 90 | 90 – 101 = –11 |
| 10 | 123 | = 100 | 100 – 123 = –23 |
Step 2: Find the profit-maximising output level
From the table, the profit is maximum at Output = 5 units, where Profit = Rs 12.
At output levels below and above 5 units, the profit is lower. Thus, the profit-maximising level of output is 5 units.
Explanation
This question tests the student's understanding of profit calculation in a perfectly competitive market. The firm is a price-taker, so TR is simply Price × Quantity. The profit-maximizing output is found by comparing profits across all output levels and identifying where profit is highest. The context confirms that profit (π) = TR – TC, and for profit maximization, the firm identifies the quantity where this difference is greatest.
Solution Steps
Step 1: Calculate Total Revenue (TR) at each output level using TR = Price × Output (Price = Rs 10)
Step 2: Calculate Profit at each output level using Profit = TR – TC
Step 3: Compare all profit values to identify the maximum profit
Step 4: Identify the output level corresponding to maximum profit (Output = 5 units, Profit = Rs 12)