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?
OK. I have considered it. What next?
a. To calculate profit for each quantity, we need to subtract the total cost from the total revenue for each quantity.
Profit = Total Revenue - Total Cost
QUANTITY | PROFIT
0 |-8
1 |-1
2 |6
3 |13
4 |19
5 |21
6 |21
7 |19
To maximize profit, the firm should produce the quantity at which the profit is the highest. Based on the table, the quantity at which the profit is the highest is 5, where the profit is $21.
b. Marginal revenue is the change in total revenue when one additional unit is sold. To calculate marginal revenue, we need to find the difference in total revenue between consecutive quantities.
Marginal Revenue = Total Revenue (at current quantity) - Total Revenue (at previous quantity)
QUANTITY | MARGINAL REVENUE
1 |8
2 |8
3 |8
4 |8
5 |8
6 |8
7 |8
Marginal cost is the change in total cost when one additional unit is produced. To calculate marginal cost, we need to find the difference in total cost between consecutive quantities.
Marginal Cost = Total Cost (at current quantity) - Total Cost (at previous quantity)
QUANTITY | MARGINAL COST
1 |1
2 |1
3 |1
4 |2
5 |6
6 |8
7 |10
To graph the marginal revenue and marginal cost, we can plot the values on a graph with the x-axis representing quantity and the y-axis representing marginal revenue and marginal cost.
The graph should show a straight line with marginal revenue staying constant at 8 for all quantities, as seen in the table above. Marginal cost, on the other hand, increases slightly as the quantity produced increases.
The curves for marginal revenue and marginal cost intersect at the quantity of 4.5 (2 1/2 in terms of whole numbers).
This intersection point is the quantity at which marginal revenue equals marginal cost. It is also the quantity at which the firm maximizes its profit. Therefore, the answer to part (a), which indicated that the firm should produce 5 units to maximize profit, is consistent with the intersection point on the graph.
c. Based on the information provided, we cannot definitively determine whether the firm is in a competitive industry or whether the industry is in a long-run equilibrium. We would need additional information, such as the number of firms in the industry, market price, and industry structure, to make a determination.