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Chapter 7: Problem 4

The following table gives the short-run and long-run total costs for various levels of output of Consolidated National Acme, Inc.: $$\begin{array}{ccc}Q & T C_{1} & T C_{2} \\\\\hline 0 & 0 & 350 \\\1 & 300 & 400 \\\2 & 400 & 435 \\\3 & 465 & 465 \\\4 & 495 & 505 \\\5 & 540 & 560 \\\6 & 600 & 635 \\\7 & 700 & 735\end{array}$$ a. Which column, \(T C_{1}\) or \(T C_{2},\) gives long-run total cost, and which gives short-run total cost? How do you know? b. For each level of output, find short-run \(T F C\) \(T V C, A F C, A V C,\) and \(M C\) c. At what output level would the firm's short-run and long-run input mixes be the same? d. Starting from producing two units, Consolidated's managers decide to double production to four units. So they simply double all of their inputs in the long run. Comment on their managerial skills. e. Over what range of output do you see economies of scale? Diseconomies of scale? Constant returns to scale?

Short Answer

Expert verified
Column \(TC_2\) shows the long-run total cost and column \(TC_1\) shows the short-run total cost. The short-run and long-run input mixes are the same at \(Q=3\). The managerial skills of Consolidated's managers are efficient as they are able to increase production without doubling the cost. Economies of scale can be seen when output increases from zero to three units. Beyond four units, we see diseconomies of scale.

Step by step solution

01

Part a: Identify Short-run and Long-run costs

Identify long-run total cost (TC2) as being the column which does not have a fixed component at zero output level (i.e. \(TC_2 = 350\) when \(Q=0\)). This is indicated by the fact that this company still has costs when no output is produced. Thus, \(TC_1\) is the short-run total cost since it doesn't reflect any costs when the output (Q) is zero.
02

Part b: Calculate TFC, TVC, AFC, AVC and MC

This part involves calculating additional cost concepts. Let's start with the total fixed cost (TFC), which is simply the cost that doesn't change with output in the short-run, so \(TFC=300\) for all Q. Total variable cost (TVC) is then calculated for each output level as the difference between the total cost and the total fixed cost. Average fixed cost (AFC) is calculated as the TFC divided by the output level, while average variable cost (AVC) is TVC divided by Q. Marginal cost (MC) is the change in total cost divided by the change in quantity.
03

Part c: Identify Output Level With Same Input Mixes

To find out at what output level the firm's short-run and long-run input mixes would be the same, look for the point where the short-run and long-run total costs are equal. This occurs when \(Q=3\), as both \(TC_1\) and \(TC_2\) are 465.
04

Part d: Analyze Managerial Skills

Looking at the data, it can be seen that when the company decides to double its output from two units to four units, the long-run total cost increases from 435 to 505 (an increase of 70 units), not by the doubling (870) as expected if the inputs were simply doubled. Therefore, the managers are successfully achieving more production without needing to double the inputs, indicating effective management skills.
05

Part e: Identify Scale Economies

Moving from \(Q=0\) to \(Q=1\), \(Q=1\) to \(Q=2\) and \(Q=2\) to \(Q=3\), there are economies of scale as total costs are increasing at a decreasing rate. From \(Q=3\) to \(Q=4\) and beyond, there appears to be constant returns to scale as total costs are increasing at a constant rate. From \(Q=4\) to \(Q=7\), there are diseconomies of scale as total costs are increasing at an increasing rate.

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Most popular questions from this chapter

Down On Our Luck Studios has spent \(\$ 100\) million producing an awful film, \(A\) Depressing Story About \(a\) Miserable Person. If the studio releases the film, the most cost-effective marketing plan would cost an additional \(\$ 5\) million, bringing the total amount spent to \(\$ 105\) million. Box office sales under this plan are predicted to be \(\$ 12\) million, which would be split evenly between the theaters and the studio. Additional studio revenue from video and DVD sales would be about \(\$ 2\) million. Should the studio release the film? If no, briefly explain why not. If yes, explain how it could make sense to release a film that cost \(\$ 105\) million but earns only \(\$ 12\) million.

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The following table shows total output (in tax returns completed per day) of the accounting firm of Hoodwink and Finagle: $$\begin{array}{cc}\text { Number of } & \text { Number of Returns } \\\\\text { Accountants } & \text { per Day } \\\\\hline 0 & 0 \\\1 & 5 \\\2 & 12 \\\3 & 17 \\\4 & 20 \\\5 & 22\end{array}$$ Assuming the quantity of capital (computers, adding machines, desks, etc.) remains constant at all output levels: a. Calculate the marginal product of each accountant. b. Over what range of employment do you see increasing returns to labor? Diminishing returns? c. Explain why \(M P L\) might behave this way in the context of an accounting firm.
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