Output
Revenue Total Cost Profit
1 90 20+1+(1) ² = 22 90-22=68
2 160 20+2+(2) ² =26 160-26=134
3 210 20+3+(3) ² =32 210-32=178
4 240 20+4+(4) ² =40 240-40=200
5 250 20+5+(5) ² =50 250-50=200
6 240 20+6+(6) ² =62 240-62=172
7 210 20+7+(7) ² =76 210-76=134
8 160 20+8+(8) ² =92 160-92=68
9 90 20+9+(9) ² =110 110-90=20
10 0 20+10+(10) ² =130 130-0=0
a) Complete the table and determine the profit-maximizing level of output.
b) Based on answer to part (a), what would happen to the firm in the long run?
To complete the table and determine the profit-maximizing level of output, we need to understand the calculations involved in determining the profit for each level of output.
The formula for profit in this case is given as follows:
Profit = Revenue - Total Cost
We can break down the calculations for Revenue and Total Cost for each level of output as follows:
For level 1:
Revenue = 1
Total Cost = 20 + 1 + (1)^2 = 22
Profit = 1 - 22 = -21
For level 2:
Revenue = 2
Total Cost = 20 + 2 + (2)^2 = 26
Profit = 2 - 26 = -24
We can continue this calculation for each level of output, until we complete the table.
For part (a), we need to fill in the table and determine the profit-maximizing level of output. Here is the complete table:
Revenue | Total Cost | Profit
------------------------------
1 | 22 | -21
2 | 26 | -24
3 | 32 | -29
4 | 40 | -36
5 | 50 | -45
6 | 62 | -56
7 | 76 | -69
8 | 92 | -84
9 | 110 | -101
10 | 130 | -120
To determine the profit-maximizing level of output, we need to look for the level at which profit is maximized. In this case, we can see that the profit is highest at level 5, where the profit is -45. Therefore, the profit-maximizing level of output is 5.
For part (b), based on the answer to part (a), we can conclude that the firm is not making any profit at the profit-maximizing level of output, which is 5. If the firm continues to operate at this level in the long run, it would not be sustainable as it is not generating any profit. In the long run, the firm may need to reassess its production and cost structure to find a level of output that is profitable or consider other strategies to improve its profitability.