6. Consider total cost and total revenue given in the table below:
QUANTITY 0 1 2 3 4 5 6 7
Total cost $8 $9 $10 $11 $13 $19 $27 $37
Total revenue 0 8 16 24 32 40 48 56
a. Calculate profit for each quantity. How much should the firm produce to maximize profit?
b. Calculate marginal revenue and marginal cost for each quantity. Graph them. (Hint: Put the points between whole numbers. For example, the marginal cost between 2 and 3 should be graphed at 2 1/2.)
At what quantity do these curves cross? How does this relate to your answer to part (a)?
c. Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in a long-run equilibrium?
To answer these questions, we need to understand some basic concepts and calculations related to profit, marginal revenue, marginal cost, and market structure.
a. Profit is calculated by subtracting total cost from total revenue. To calculate profit for each quantity:
Profit = Total Revenue - Total Cost
QUANTITY Total Cost Total Revenue Profit
0 $8 0 -$8
1 $9 8 -$1
2 $10 16 $6
3 $11 24 $13
4 $13 32 $19
5 $19 40 $21
6 $27 48 $21
7 $37 56 $19
To maximize profit, the firm should produce the quantity at which profit is highest. In this case, the highest profit is $21, which occurs at both quantities 5 and 6. Therefore, the firm should produce either 5 or 6 units to maximize profit.
b. Marginal revenue (MR) is the additional revenue earned from producing one additional unit of output. It is calculated by taking the change in total revenue divided by the change in quantity.
Marginal revenue = ΔTotal Revenue / ΔQuantity
Marginal cost (MC) is the additional cost incurred from producing one additional unit of output. It is calculated by taking the change in total cost divided by the change in quantity.
Marginal cost = ΔTotal Cost / ΔQuantity
QUANTITY Total Cost Total Revenue Profit MR MC
1 $9 8 -$1 $8 $9-$0 = $9
2 $10 16 $6 $8 $10-$9 = $1
3 $11 24 $13 $8 $11-$10 = $1
4 $13 32 $19 $8 $13-$11 = $2
5 $19 40 $21 $8 $19-$13 = $6
6 $27 48 $21 $8 $27-$19 = $8
7 $37 56 $19 $8 $37-$27 = $10
Graphing the MR and MC curves:
X-axis represents quantity, and Y-axis represents MR and MC.
MR curve:
Points: (0, $8), (1, $8), (2, $8), (3, $8), (4, $8), (5, $8), (6, $8), (7, N/A)
Line: Straight horizontal line at a height of $8.
MC curve:
Points: (0, N/A), (1, $9), (2, $1), (3, $1), (4, $2), (5, $6), (6, $8), (7, N/A)
Line: Starts at (1, $9), goes down to (2, $1), stays horizontal at $1 until (5, $6), and then constant at $8.
The MR and MC curves cross at quantity 6 (approximately 6.5). This indicates that at quantity 6, marginal revenue is equal to marginal cost. This point is known as the profit-maximizing level of output.
This result aligns with the answer in part (a) – the firm should produce either 5 or 6 units to maximize profit.
c. To determine whether the firm is in a competitive industry and if the industry is in a long-run equilibrium, we need additional information about market structure and long-run adjustment processes. The table alone does not provide sufficient data to make a definitive judgment about the firm's market structure and long-run equilibrium. Factors such as the number of firms in the market, entry and exit barriers, and concentration ratios are essential for making such determinations. Additional information is needed to answer this question.