. 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?
a) 1=-8/2=-1/3=6/4=19/5=21/6=21/7=19
maximizing profit is at a quantity of 5 or 6
b)
MR: 0,8,8,8,8,8,8,8
MC: 1,1,1,2,6,8,10
Profit maximizing point at 6 because there MC equals MR.
c) the firm is in a competitive industry because price stays the same (horizontal) at any quantity produced
--> not in a long run equilibrium because price(8€) exceeds average total cost (4,50€)
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
Consider total cost and total revenue given in the following table:
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 21 ⁄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?
a. To calculate profit, subtract the total cost from the total revenue for each quantity:
Profit = Total Revenue - Total Cost
QUANTITY 0: Profit = $0 - $8 = -$8
QUANTITY 1: Profit = $8 - $9 = -$1
QUANTITY 2: Profit = $16 - $10 = $6
QUANTITY 3: Profit = $24 - $11 = $13
QUANTITY 4: Profit = $32 - $13 = $19
QUANTITY 5: Profit = $40 - $19 = $21
QUANTITY 6: Profit = $48 - $27 = $21
QUANTITY 7: Profit = $56 - $37 = $19
To maximize profit, the firm should produce the quantity at which the profit is highest. From the calculations above, the firm should produce either quantity 5 or 6 to maximize profit, as they both have a profit of $21.
b. To calculate marginal revenue, find the change in total revenue when quantity increases by 1:
Marginal Revenue = Change in Total Revenue / Change in Quantity
QUANTITY 0-1: Marginal Revenue = ($8 - $0) / (1 - 0) = $8
QUANTITY 1-2: Marginal Revenue = ($16 - $8) / (2 - 1) = $8
QUANTITY 2-3: Marginal Revenue = ($24 - $16) / (3 - 2) = $8
QUANTITY 3-4: Marginal Revenue = ($32 - $24) / (4 - 3) = $8
QUANTITY 4-5: Marginal Revenue = ($40 - $32) / (5 - 4) = $8
QUANTITY 5-6: Marginal Revenue = ($48 - $40) / (6 - 5) = $8
QUANTITY 6-7: Marginal Revenue = ($56 - $48) / (7 - 6) = $8
To calculate marginal cost, find the change in total cost when quantity increases by 1:
Marginal Cost = Change in Total Cost / Change in Quantity
QUANTITY 0-1: Marginal Cost = ($9 - $8) / (1 - 0) = $1
QUANTITY 1-2: Marginal Cost = ($10 - $9) / (2 - 1) = $1
QUANTITY 2-3: Marginal Cost = ($11 - $10) / (3 - 2) = $1
QUANTITY 3-4: Marginal Cost = ($13 - $11) / (4 - 3) = $2
QUANTITY 4-5: Marginal Cost = ($19 - $13) / (5 - 4) = $6
QUANTITY 5-6: Marginal Cost = ($27 - $19) / (6 - 5) = $8
QUANTITY 6-7: Marginal Cost = ($37 - $27) / (7 - 6) = $10
To graph the marginal revenue and marginal cost, plot the points:
Marginal Revenue: (0, $8), (1, $8), (2, $8), (3, $8), (4, $8), (5, $8), (6, $8)
Marginal Cost: (0, $1), (1, $1), (2, $1), (3, $2), (4, $6), (5, $8), (6, $10)
The curves of marginal revenue and marginal cost cross at the quantity of 5. This means that the quantity of 5 is the point at which the marginal revenue equals the marginal cost. This relates to the previous answer in part (a), as it confirms that producing quantity 5 would maximize profit.
c. From the given information, we cannot definitively tell whether the firm is in a competitive industry or whether the industry is in a long-run equilibrium. Further information, such as market structure and the behavior of other firms in the industry, would be needed to make such determinations.
a. To calculate profit for each quantity, we need to subtract the total cost from the total revenue. The profit formula is:
Profit = Total Revenue - Total Cost
Using the given data, we can calculate the profits for each quantity:
QUANTITY | 0 1 2 3 4 5 6 7
--------------------------------------------
Profit | 0 -1 6 13 19 21 21 19
To find the quantity that maximizes profit, we look for the highest profit value, which occurs at a quantity of 6. Therefore, the firm should produce a quantity of 6 units to maximize profit.
b. Marginal revenue (MR) is the change in total revenue for each additional unit produced. It is calculated by finding the difference in total revenue between consecutive quantities. Marginal cost (MC) is the change in total cost for each additional unit produced. It is calculated by finding the difference in total cost between consecutive quantities.
QUANTITY | 0 1 2 3 4 5 6 7
--------------------------------------------
MR | 8 8 8 8 8 8 8
MC | 1 1 1 2 6 8 10
To graph MR and MC, we plot the values as points on a graph. The x-axis represents the quantity, and the y-axis represents the marginal revenue or marginal cost.
MR points: (0, 8), (1, 8), (2, 8), (3, 8), (4, 8), (5, 8), (6, 8), (7, 8)
MC points: (0, 1), (1, 1), (2, 1), (3, 2), (4, 6), (5, 8), (6, 10)
When we graph these points, we can see that the MR curve is a horizontal line at a height of 8, while the MC curve starts low, increases, and eventually crosses the MR line. The point at which the MC curve intersects the MR line is at a quantity of 4.5.
c. To determine if the firm is in a competitive industry, we need to analyze the data further. Since we only have information about the cost and revenue of the individual firm, it is difficult to determine whether the industry as a whole is competitive. However, we can look at whether the firm is making a profit or a loss.
In this case, when looking at the profit values, we can see that the firm is making a positive profit at all quantities except for 1. Since the firm is making a profit, it suggests that they have some degree of market power, which might indicate it is not a perfectly competitive industry.
Determining whether the industry is in long-run equilibrium requires more information. We would need to consider factors such as entry and exit of firms, whether the industry is operating at its efficient scale, and whether there are any barriers to entry. Without this additional information, we cannot definitively determine if the industry is in a long-run equilibrium.