In the short run a firm needs six units of labor to produce eight units of output and ten units of labor to produce nine units of output. If the price of labor is $2 per unit, what is the marginal cost of the ninth unit of output?
To find the marginal cost of the ninth unit of output, we need to calculate the change in total cost when the firm increases its output from eight units to nine units.
To do this, we can first find the cost of labor for each level of output using the given information:
- For the first scenario, where 6 units of labor produce 8 units of output, the cost of labor is 6 units x $2 per unit = $12.
- For the second scenario, where 10 units of labor produce 9 units of output, the cost of labor is 10 units x $2 per unit = $20.
Now, we can calculate the change in total cost by subtracting the cost of labor for producing 8 units of output from the cost of labor for producing 9 units of output:
Change in total cost = Cost of labor for 9 units of output - Cost of labor for 8 units of output
= $20 - $12
= $8.
Therefore, the marginal cost of the ninth unit of output is $8.