The marketing division of a firm has measured demand for its product and reports that it is Q = 24 – P, where Q is units and P is price per unit in dollars. The cost is given in the table below. Complete the table and determine the profit-maximizing level of output for this firm.
Output Total Cost Price per unit Revenue Profit
0 10
1 18
2 20
3 22
4 25
5 29
6 34
7 40
8 48
Output Total Cost Price Revenue Profit
0 10 24 0 -10
1 18 22 22 4
2 20 20 40 20
3 22 18 54 32
4 25 16 64 30
5 29 14 70 41
6 34 12 72 38
7 40 10 70 30
8 48 8 64 16
To determine the profit-maximizing level of output for this firm, we need to calculate the revenue and profit for each level of output and find the level that maximizes profit.
First, let's calculate the revenue for each level of output using the given price per unit:
Output Price per unit Revenue
0 - -
1 - -
2 - -
3 - -
4 - -
5 - -
6 - -
7 - -
8 - -
To calculate the revenue, we multiply the price per unit by the quantity:
Revenue = Price per unit * Output
Now, let's calculate the total cost for each level of output using the given total cost:
Output Total Cost
0 -
1 -
2 -
3 -
4 -
5 -
6 -
7 -
8 -
Now, we need to find the profit for each level of output:
Profit = Revenue - Total Cost
Finally, let's complete the table:
Output Total Cost Price per unit Revenue Profit
0 10 - - -
1 18 - - -
2 20 - - -
3 22 - - -
4 25 - - -
5 29 - - -
6 34 - - -
7 40 - - -
8 48 - - -
To find the revenue for each level of output, we use the demand equation given as Q = 24 - P, where Q is the quantity and P is the price per unit.
For example:
- For Output 0, the price per unit is unknown, so we can't calculate revenue.
- For Output 1, using the demand equation, we can calculate the price per unit by substituting Q = 1:
1 = 24 - P
P = 24 - 1 = 23
Revenue = Price per unit * Output = 23 * 1 = 23
- Repeat the above steps for the remaining levels of output to calculate the revenue, total cost, and profit.
Once you've completed the table, you can find the profit-maximizing level of output by identifying the output level where profit is maximized. This is the output level that generates the highest profit value.