March 27, 2017

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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?

  • Economics - ,

    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.

  • Economics - ,

    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.

  • Economics - ,

    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!

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