The following table gives the short-run and long-run total...

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?

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?

Key Concepts

Returns to Scale

Returns to scale examine the relationship between the proportional increase in inputs and the resulting change in output. If doubling all inputs leads to more than double the output, economies of scale are present; if output exactly doubles, there are constant returns to scale; and if output increases by less than double, diseconomies of scale occur. This concept is essential for understanding how cost structures change with the scale of production.

Input Scaling and Managerial Implications

Doubling all inputs to double output reflects a scenario of constant returns to scale, where the proportional increase in inputs leads to a proportional increase in production. Managerial decisions based on this assumption require careful consideration, as practical environments may exhibit non-linearities in cost behavior. Evaluating whether such scaling is effective involves verifying the actual performance of the cost function against the theoretical expectations of proportionality.

Short-Run versus Long-Run Cost Analysis

This concept distinguishes between periods in which some factors of production are fixed (short run) and those in which all inputs can be varied (long run). In the short run, firms incur fixed costs that do not change with the level of output, while in the long run, all costs become variable as the firm can adjust all input levels, allowing a different cost structure.

Cost Components (Fixed, Variable, Average, and Marginal Costs)

Understanding production costs requires decomposing total costs into fixed and variable components. Total Fixed Costs (TFC) remain constant regardless of output, while Total Variable Costs (TVC) change with the quantity produced. Average Fixed Cost (AFC) and Average Variable Cost (AVC) are computed by dividing TFC and TVC by output, respectively, and the Marginal Cost (MC) represents the additional cost incurred when producing one additional unit of output.

Efficient Scale and the Short-Run/Long-Run Cost Intersection

The point where the short-run cost structure (which includes fixed costs) equals the long-run cost structure (with all costs variable) indicates the efficient scale of production. At this output level, the firm's combination of inputs in the short run aligns with the long-run input mix, thereby minimizing cost and maximizing efficiency under optimal production conditions.

Transcript

00:01 Today we'll be solving problem four from chapter seven of principles and applications of microeconomics.

00:06 This question gives us a company consolidated national acme, inc.

00:11 And it also gives us the quantity produced and two variables for total cost, total cost one and total cost two.

00:17 I've copied those values here into an excel sheet.

00:20 And the first part of the question wants to know which one of these is the long run cost curve and which one of them is the short run cost curve.

00:27 And there's sort of three ways that we know this.

00:29 So first of all, the long -run cost is always less than the short -run cost at the same quantity.

00:36 So as you can see, total cost 1 is always less than total cost 2 at the same quantity.

00:42 So we know from that alone that total cost 1 is the long -run cost curve.

00:48 So we're going to go ahead and label them.

00:53 Total cost 1 is the long -run cost curve, and total cost 2 is the short -run cost curve.

00:57 However, there's also a few other ways to know.

01:00 So there's no fixed cost for the long run at the zero -with unit.

01:04 And we can see that here that at the zero -with unit, the long -run total cost curve doesn't have a fixed cost.

01:10 The third way that we can know this is if we look at the long -run average total cost curves and the short -run average total cost curves.

01:18 So in order to calculate that, we're going to do the long -run average total cost curve and the short -run average total cost curve by dividing the long run cost curve by the quantity and doing the same thing for the short run cost curve.

01:39 Now obviously at zero we don't have a average total cost curve, but we know that the long run average total cost curve is always going to be an envelope of the short run average total cost curve.

01:52 So if we go ahead and plot these, we can see that the long run average total cost curve in blue is an envelope of the short run average total cost curve.

02:05 Part b if the question would like us to use the short run total cost curve to calculate the total fixed cost, total variable cost, average fixed cost, average variable cost, and marginal cost for each quantity.

02:18 So we know that the cost at the zero with unit is going to be the fixed cost.

02:23 So our total fixed cost at the zero with unit is going to be 350.

02:27 And since this is a fixed cost through all of the quantities, this is going to be our fixed cost for 037.

02:33 In order to calculate the total variable cost, we want to, subtract the fixed cost from our short run total cost.

02:42 So at the zero with unit our variable cost is zero, but as we move this formula down, we can see that our variable cost is going to be the short run total cost minus the total fixed cost...

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