Yes, I can help answer the questions. Let's go through each question step by step.
A.) To find the price of capital, we can use the expansion path. The expansion path hits the lines at different levels of output. We are given that at the output level of 120, the capital units (C) is 20. Since the capital units increase by 10 as the output increases by 60 (from 120 to 180), we can infer that for every 60 increase in output, the capital units increase by 10.
Therefore, at the output level of 180, the capital units (C) would be 20 + 10 = 30. Similarly, at the output level of 240, the capital units (C) would be 30 + 10 = 40.
Since we know that the price of labor is $100 per unit, we can assume that the price of capital will increase by the same proportion. So, if the labor price is $100 per unit, the capital price would be $100 per unit as well.
Therefore, the price that Impact Industries pays for capital is $100 per unit.
B.) To minimize total costs at an output level of 180, we need to find the combination of labor and capital that corresponds to the expansion path. From the information given, at the output level of 180, the capital units (C) is 40 and the labor units (L) is 6.
Therefore, at an output level of 180, Impact Industries should use 40 units of capital and 6 units of labor to minimize total costs.
C.) To calculate the total cost of producing 120, 180, and 240 units of output in the long run, we need to multiply the respective units of capital and labor with their respective prices.
For 120 units of output: Total cost = (20 units of capital * price of capital) + (4 units of labor * price of labor)
For 180 units of output: Total cost = (40 units of capital * price of capital) + (6 units of labor * price of labor)
For 240 units of output: Total cost = (50 units of capital * price of capital) + (8 units of labor * price of labor)
D.) In the short run, with capital fixed, the firm should expand output by increasing the usage of labor. From the information given, when the capital is fixed at 40 units (corresponding to an output level of 180), the labor units increase by 2 for every 60 increase in output.
Therefore, to expand production to 240 units (an increase of 60 from 180), the labor units should increase by 2. So, the labor units would be 6 + 2 = 8.
Since the capital is fixed at 40 units, the amount of labor used will be 8 units, and the amount of capital used will remain at 40 units.
E.) To calculate the average variable cost (AVC), average fixed cost (AFC), and average total cost (ATC) in the short run, we need to use the formula:
AVC = Total variable cost / Output
AFC = Total fixed cost / Output
ATC = Total cost / Output
We already have the total cost for each output level from part C. Now we just need to divide those costs by the respective output levels.
AVC for 120 units of output = Total cost for 120 units of output / 120 units of output
AVC for 180 units of output = Total cost for 180 units of output / 180 units of output
AVC for 240 units of output = Total cost for 240 units of output / 240 units of output
Similarly, we can calculate AFC and ATC using the respective formulas.
I hope this helps!