Problem 8.1 - Profit maximization: TR – TC approach Problem: A competitive firm's short-run cost information is shown in the table below. Output | Fixed Cost | Variable Cost | Total Cost | 0 | $9.00 | $ 0.00 | $ 9.00 | 1 | 9.00 | 8.00 | 17.00 | 2 | 9.00 | 15.00 | 24.00 | 3 | 9.00 | 21.00 | 30.00 | 4 | 9.00 | 26.00 | 35.00 | 5 | 9.00 | 32.00 | 41.00 | 6 | 9.00 | 39.00 | 48.00 | 7 | 9.00 | 47.00 | 56.00 | 8 | 9.00 | 56.00 | 65.00 | 9 | 9.00 | 66.00 | 75.00 | 10 | 9.00 | 77.00 | 86.00 |
- Suppose the firm can sell all the output it desires at the market price of $9.10. Compute the firm's total revenue and its total profit (loss) for the potential output choices shown in the table. What output level maximizes the firm's profits (or minimizes its losses)?
- Repeat part a. assuming the price has fallen to $7.10.
| Answer: - The table showing revenue, cost, and profit is completed below. Total revenue is found as price times output level. For example, total revenue at an output level of 3 is $9.10 x 3 = $27.30. Total profit is equal to total revenue minus total cost. At 3 units of output, profit = $27.30 – $30.00 = –2.70
Output | Total Cost | Total Revenue | Total Profit | 0 | $ 9.00 | $ 0.00 | –$ 9.00 | 1 | 17.00 | 9.10 | –7.90 | 2 | 24.00 | 18.20 | –5.80 | 3 | 30.00 | 27.30 | –2.70 | 4 | 35.00 | 36.40 | 1.40 | 5 | 41.00 | 45.50 | 4.50 | 6 | 48.00 | 54.60 | 6.60 | 7 | 56.00 | 63.70 | 7.70 | 8 | 65.00 | 72.80 | 7.80 | 9 | 75.00 | 81.90 | 6.90 | 10 | 86.00 | 91.00 | 5.00 |
Total profit is maximized at 8 units of output. - The new table is presented below:
Output | Total Cost | Total Revenue | Total Profit | 0 | $ 9.00 | $ 0.00 | $–9.00 | 1 | 17.00 | 7.10 | –9.90 | 2 | 24.00 | 14.20 | –9.80 | 3 | 30.00 | 21.30 | –8.70 | 4 | 35.00 | 28.40 | –6.60 | 5 | 41.00 | 35.50 | –5.50 | 6 | 48.00 | 42.60 | –5.40 | 7 | 56.00 | 49.70 | –6.30 | 8 | 65.00 | 56.80 | –8.20 | 9 | 75.00 | 63.90 | –11.10 | 10 | 86.00 | 71.00 | –15.00 |
The loss is minimized at an output of 6 units. Even though this output level entails a loss, the loss would be even greater if the firm shut down and produced no output.
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Problem 8.2 - Profit maximization: MR = MC approach Problem: Suppose a competitive firm's cost information is as shown in the table below. Its total fixed cost is $9.00. Output | Marginal Cost | Average Variable Cost | Average Total Cost | 0 | | | | 1 | $ 8.00 | $8.00 | $17.00 | 2 | 7.00 | 7.50 | 12.00 | 3 | 6.00 | 7.00 | 10.00 | 4 | 5.00 | 6.50 | 8.75 | 5 | 6.00 | 6.40 | 8.20 | 6 | 7.00 | 6.50 | 8.00 | 7 | 8.00 | 6.71 | 8.00 | 8 | 9.00 | 7.00 | 8.13 | 9 | 10.00 | 7.33 | 8.33 | 10 | 11.00 | 7.70 | 8.60 |
- Suppose the firm sells its output at a price of $9.10. What is the firm's marginal revenue (MR)?
- Compare MR to marginal cost (MC) to determine the firm's profit maximizing (loss-minimizing) output level. Be sure to check whether or not the firm should shut down.
- What is the firm's per-unit profit (loss) at this output level?
- What is the firm's total profit (loss) at this output level?
- Repeat parts a. through d. assuming the price has fallen to $7.10.
- Repeat again assuming the price has fallen to $6.10
| Answer: - Marginal revenue is equal to price, or $9.10 in this instance.
- The firm will expand production as long as MR exceeds MC and price exceeds average variable cost. It produces 8 units to maximize profits.
- Per-unit profit is equal to average revenue, or price, minus average total cost. Per-unit profit = $9.10 – $8.13 = $.97.
- Total profit is equal to per unit profit ($.97) times the number sold (8). Profit = $7.76.
- MR = price = $7.10. Comparing to MC, the firm produces 6 units. The firm's per unit loss is $7.10 – $8.00 = –$.90. Since this is negative, check to see if price exceeds average variable cost. At 6 units of output, AVC = $6.50, which is indeed less than price, so the firm should produce 6 rather than shut down. The firm's total loss is $.90 x 6 = $5.40. The firm would lose an amount equal to its fixed cost ($9.00) if it were to shut down.
- Marginal revenue is $6.10. This is lower than the lowest possible value of average variable cost, so the firm should shut down, losing an amount equal to its fixed cost, or $9.00.
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Problem 8.3 - Short-run competitive equilibrium Problem: A competitive firm's short-run cost information is shown in the table below. Output | Marginal Cost | Average Variable Cost | Average Total Cost | 0 | | | | 1 | $ 8.00 | $8.00 | $17.00 | 2 | 7.00 | 7.50 | 12.00 | 3 | 6.00 | 7.00 | 10.00 | 4 | 5.00 | 6.50 | 8.75 | 5 | 6.00 | 6.40 | 8.20 | 6 | 7.00 | 6.50 | 8.00 | 7 | 8.00 | 6.71 | 8.00 | 8 | 9.00 | 7.00 | 8.13 | 9 | 10.00 | 7.33 | 8.33 | 10 | 11.00 | 7.70 | 8.60 |
- If the market price is $5.25, how much will this firm produce? Enter in the second column of the table below. Repeat for the remaining prices shown in the table.
Price | Quantity Supplied, This Firm | Quantity Supplied, 2000 Firms | Quantity Demanded | $5.25 | | | 20,000 | $6.25 | | | 18,000 | $7.25 | | | 16,000 | $8.25 | | | 14,000 | $9.25 | | | 12,000 | $10.25 | | | 10,000 |
- Fill in the next column to determine the market supply in this industry, assuming there are 2000 identical firms in the industry.
Further suppose that the market demand schedule for this industry is given by the last column in the table. - What is the equilibrium quantity in this market?
- What is the equilibrium price in this market?
- What are the resulting output, revenue, cost, and profit of the typical firm?
| Answer: - At prices below $6.40, the price is less than minimum average variable cost, so the firm shuts down, producing zero. For other prices, the firm produces at the output corresponding to MR = MC. The table is completed below:
Price | Quantity Supplied, This Firm | Quantity Supplied, 2000 Firms | Quantity Demanded | $5.25 | 0 | 0 | 20,000 | $6.25 | 0 | 0 | 18,000 | $7.25 | 6 | 12,000 | 16,000 | $8.25 | 7 | 14,000 | 14,000 | $9.25 | 8 | 16,000 | 12,000 | $10.25 | 9 | 18,000 | 10,000 |
- Each value in the third column is 2000 times the value in the second column: total quantity supplied in the market is equal to the number of firms multiplied by the amount produced by the typical firm.
- Equilibrium quantity is 14,000 units, where market quantity demanded equals quantity supplied.
- Equilibrium price is $8.25, corresponding to the equilibrium quantity.
- At a market price of $8.25, the typical firm produces 7 units. Its revenue is $8.25 x 7 = $57.75. Its total cost is $56, equal to its output times its average total cost: $56 = 7 x $8. Its profit is the difference between total revenue and total cost: profit = $57.75 – $56 = $1.75. Alternatively, its profit is equal to output times the difference between price and average total cost: 7 x ($8.25 – $8.00) = $1.75.
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