consider total cost and total revenue given in the table bellow:
quantity total cost total revenue
0 $8 0
1 $9 8
2 $10 16
3 $11 24
4 $13 32
5 $19 40
6 $27 48
7 $37 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?
An Excel spreadsheet is very helpful for these kinds of problems.
Always always always, maximize where MC=MR.
So calculate marginal cost and marginal revenue schedules. Going from 0 to 1 unit, costs went from 8 to 9, so MC here is 1. (Take the hint and MC at 1/2 is 1). Going from 0 to 1 unit, total revenues went from 0 to 8, so TR is 8.
Repeat for the remaining units of production -- find where MC=MR.
c) Since MR is constant, the firm must be in a competitive industry. I don't think there is enough info to determine whether the industry in in a long-run equilibrium
please i need your help ^_^
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. To calculate profit, we subtract total cost from total revenue for each quantity:
Quantity 0: Profit = Total Revenue - Total Cost = 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
From these calculations, we can see that the firm should produce the quantity where the profit is maximized. In this case, the firm should produce either quantity 5 or 6, as they both have the highest profit of 21.
b. To calculate marginal revenue and marginal cost for each quantity, we need to find the difference in total revenue and total cost between consecutive quantities:
Marginal Revenue:
Quantity 0 to 1: Marginal Revenue = Total Revenue for Quantity 1 - Total Revenue for Quantity 0 = 8 - 0 = 8
Quantity 1 to 2: Marginal Revenue = 16 - 8 = 8
Quantity 2 to 3: Marginal Revenue = 24 - 16 = 8
Quantity 3 to 4: Marginal Revenue = 32 - 24 = 8
Quantity 4 to 5: Marginal Revenue = 40 - 32 = 8
Quantity 5 to 6: Marginal Revenue = 48 - 40 = 8
Quantity 6 to 7: Marginal Revenue = 56 - 48 = 8
Marginal Cost:
Quantity 0 to 1: Marginal Cost = Total Cost for Quantity 1 - Total Cost for Quantity 0 = 9 - 8 = 1
Quantity 1 to 2: Marginal Cost = 10 - 9 = 1
Quantity 2 to 3: Marginal Cost = 11 - 10 = 1
Quantity 3 to 4: Marginal Cost = 13 - 11 = 2
Quantity 4 to 5: Marginal Cost = 19 - 13 = 6
Quantity 5 to 6: Marginal Cost = 27 - 19 = 8
Quantity 6 to 7: Marginal Cost = 37 - 27 = 10
To graph the marginal revenue and marginal cost, we can plot the points on a graph with the quantity on the x-axis and marginal revenue/marginal cost on the y-axis. Connecting the points will result in marginal revenue and marginal cost curves.
c. The point where the marginal revenue and marginal cost curves cross is the quantity where the firm maximizes its profit. From the calculations in part (a), we found that the firm should produce either quantity 5 or 6 to maximize profit. Therefore, the curves should cross at either quantity 5 or 6.
Based on the information provided, we cannot determine whether the firm is in a competitive industry or whether the industry is in long-run equilibrium.
To calculate profit for each quantity, we can subtract total cost from total revenue. The formula for profit is:
Profit = Total Revenue - Total Cost
So, let's calculate the profit for each quantity using the given table:
Quantity: 0
Profit = Total Revenue - Total Cost
Profit = 0 - 8 = -8
Quantity: 1
Profit = Total Revenue - Total Cost
Profit = 8 - 9 = -1
Quantity: 2
Profit = Total Revenue - Total Cost
Profit = 16 - 10 = 6
Quantity: 3
Profit = Total Revenue - Total Cost
Profit = 24 - 11 = 13
Quantity: 4
Profit = Total Revenue - Total Cost
Profit = 32 - 13 = 19
Quantity: 5
Profit = Total Revenue - Total Cost
Profit = 40 - 19 = 21
Quantity: 6
Profit = Total Revenue - Total Cost
Profit = 48 - 27 = 21
Quantity: 7
Profit = Total Revenue - Total Cost
Profit = 56 - 37 = 19
To maximize profit, the firm should produce the quantity that results in the highest profit. From the table, we can see that the firm should produce either 5 or 6 units to maximize profit, as these quantities have the highest profit of 21.
Now let's move on to part B, calculating marginal revenue and marginal cost.
Marginal Revenue (MR) is the change in total revenue as a result of producing an additional unit, and Marginal Cost (MC) is the change in total cost as a result of producing an additional unit.
To calculate the marginal revenue for each quantity, we can find the difference between total revenue of the current quantity and the previous quantity.
For example, the marginal revenue between 0 and 1 units is $8 (Total Revenue at 1 unit) - $0 (Total Revenue at 0 units) = $8.
Using this method, we can calculate the marginal revenue for all quantities:
Quantity: Marginal Revenue
0 to 1: $8
1 to 2: $8
2 to 3: $8
3 to 4: $8
4 to 5: $8
5 to 6: $8
6 to 7: $8
Since marginal revenue remains constant at $8 for each additional unit produced, the marginal revenue curve will be a horizontal line at $8 on the graph.
Now let's calculate the marginal cost for each quantity. We can find the difference between total cost of the current quantity and the previous quantity.
For example, the marginal cost between 0 and 1 units is $9 (Total Cost at 1 unit) - $8 (Total Cost at 0 units) = $1.
Using this method, we can calculate the marginal cost for all quantities:
Quantity: Marginal Cost
0 to 1: $1
1 to 2: $1
2 to 3: $1
3 to 4: $2
4 to 5: $6
5 to 6: $8
6 to 7: $8
To graph marginal revenue and marginal cost, we can plot the points based on the quantities and their respective marginal values on a graph. The x-axis represents quantity, and the y-axis represents dollars.
The graph will have two lines – one for marginal revenue and one for marginal cost. On the x-axis, we can place the quantities, and on the y-axis, we can place the marginal values.
To determine where the marginal revenue and marginal cost curves cross, we can find the quantity at which the two values are equal. From the calculations above, we can see that the marginal revenue and marginal cost are equal at every quantity, as the marginal revenue is always $8 and the marginal cost is always less than or equal to $8.
This indicates that the firm is operating in a competitive industry, where prices are determined by supply and demand. Furthermore, the industry appears to be in a long-run equilibrium, as the profit-maximizing quantity (5 or 6 units) coincides with the quantity at which marginal revenue and marginal cost are equal.