There is a graph showing the expansion path and three curves at 120, 180, 240 output levels.The expansion path hits these lines at(120) 20 (C)(capital units) 4(L)(Labor units, (180) 40 (C) 6(L), (240) 50(C) 8(L). There are three straight lines in faded gray that run with these curves...(120) 40(C) to 8(L), (180) 60(C) to 12(L), (240) 90 (C) to 18 (L)...I hope this helps recreate the graph?

Capital runs by 10's to 100 on the left-vertically and Labor runs by 2's to 20 horizontally

The production engineers at Impact Industries have derived the expansion path shown in the following figure described above. The price of labor is $100 per unit.

A.) What price does Impact Industries pay for capital?
B.) If the manager at Impact decides to produce 180 units of output, how much labor and capital should be used in order to minimize total costs?
C.) What is the total cost of producing 120, 180 and 240 units of output in the long run?
D.) Impact Industries originally built the plant (i.e. purchased the amount of capital) designed to produce 180 units operatimally. In the short run with capital fixed, if the manager decides to expand production to 240 units, what is the amount of labor and capital that will be used? (Hint: How must the firm expand output in the short run when capital is fixed?)
E.) Given your answer to part d, calculate the average variable, average fixed, and average total cost in the short run.

Can you help Economyst?

ok,I think I understand your graph description.

The three curves are isoquants, showing the mix of L and C that could be combined to produce a particular level of output. The three straight lines are budget constraints, showing the amounts of L and C that could be used given a fixed budget.

I presume that expansion path line goes exactly through the points where the Isoquant is tangent (touches) the budget constraint. If NO, then I don't understand your graph and my answers are null and void.

A) pick a budget constraint, say the first. The constraint touches the L axis at 8. So, with this constraint, the budget is 8*100 = $800. The constraint touches the C axis at 40. Ergo, price of C is 800/40 = $20
B) On the expansion path where the 180-Isoquat touches the budget constraint; C=40 and L=6
C) At the 180-production total cost is 40*20 + 6*100. = 1400. Repeat for the 120 level and the 240 level.
D) The optimal level of C at 180-production is 40. Draw a horizontal line at C=40. Where does the line hit the 240-Isoquant? This is the amount of L needed to produce output at 240 with C fixed at 40.
E) Variable costs are L*$100, fixed costs are C*$20. Take the L under D. AVC=L*100/240. AFC = (40)*20/240. ATC= ((L*100)+(40*20))/240.

I have to say that I like to check my answers with yours before I submit an assignment. You are a wonderful resource for anyone that is unsure about their answers. On this one, I know that it is difficult not having the graph, and you are only using the information that you are given, but just so you, or anyone reading this knows, if you check the graph capital actually hits 180 units of output at 30 units for the optimal level. I would hope that everone that is using your site is checking thier answers, and not just copying from here.

I really appreciate all the help this site provides. I agree check the figures that are given since the person posting the question may type the wrong number such as above. Thank you very much-it helps me think though the answers. Not sure I would even know where to start otherwise.

Great site!

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!