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Chapter 10

Costs

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TABLE 10-1

The Short-Run Production Function for Kelly’s Cleaners

The entries in each row of the right column tell the quantity of output produced by the quantity of variable input in the corresponding row of the left column. This production function initially exhibits increasing, then diminishing, returns to the variable input.

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TABLE 10-2

Outputs and Costs

The fixed cost of capital is $30/hr, and the cost per unit of the variable factor (L) is $10/hr. Total cost is calculated as the sum of fixed cost and variable cost.

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FIGURE 10-1

Output as a Function of One Variable Input

This production process shows increasing marginal productivity of the variable input up to L = 4, and diminishing marginal productivity thereafter.

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FIGURE 10-2The Total, Variable, and Fixed Cost Curves

These curves are for the production function for Kelly’s Cleaners, shown in Figure 10-1. The variable cost curve passes through the origin, which means that the variable cost of producing zero units of output is equal to zero. The TC curve, which is the sum of the FC and VC curves, is parallel to the VC curve and lies FC = $30/hour above it.

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FIGURE 10-3

The Production Function Q = 3KL, with K = 4

This short-run production function exhibits constant returns to L over the entire range of L. There is neither a region of increasing returns nor a region of diminishing returns to L.

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FIGURE 10-4The Total, Variable, and Fixed Cost Curves for the Production Function Q = 3KL

With K fixed at 4 machine-hr/hr in the short run and a price of K of r = $2/machine-hr, fixed costs are $8/hr. To produce Q units of output per hour requires Q/12 person-hr/hr of labour. With a price of labour of $24/person-hr, variable cost is $2Q/hr. Total cost is $8/hr + $2Q/hr.

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FIGURE 10-5The Marginal, Average Total, Average Variable, and Average Fixed Cost Curves

The MC curve intersects the ATC and AVC curves at their respective minimum points. With TC curves having this form, it is always the case that minimum MC occurs to the left of minimum AVC, which is left of minimum ATC.

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Table 10-3

Outputs and Costs

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FIGURE 10-6Quantity vs. Average Costs

ATC is the sum of AVC and AFC. AFC is declining for all values of Q.

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FIGURE 10-7

Cost Curves for a Specific Production Process

For production processes with constant marginal cost, average variable cost and marginal cost are identical. Marginal cost always lies below ATC for such processes.

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FIGURE 10-8

The Minimum-Cost Production Allocation

To produce a given total output at minimum cost, it should be allocated across production activities so that the marginal cost of each activity is the same. Horizontal summation of the MCA and MCB functions gives the MCT function.

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FIGURE 10-9

The Relationship Between MPL, APL, MC, and AVC

Normally, the MC and AVC curves are plotted with Q on the horizontal axis. In the bottom panel, they are shown as functions of L. The value of Q that corresponds to a given value of L is found by multiplying L times the corresponding value of APL. The maximum value of the MPL curve, at L = L1, top panel, corresponds to the minimum value of the MC curve, at Q = Q1, bottom panel. Similarly, the maximum value of the APL curve, at L = L2, top panel, corresponds to the minimum value of the AVC curve, at Q = Q2, bottom panel.

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FIGURE 10-10

The Isocost Line

For given input prices (r = 2 and w = 4 in the diagram), the isocost line is the locus of all possible input bundles that can be purchased for a given level of total expenditure C ($200 in the diagram). The slope of the isocost line is the negative of the input price ratio, –w/r.

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FIGURE 10-11

The Maximum Output for a Given Expenditure

A firm that is trying to produce the largest possible output for an expenditure of C will select the input combination at which the isocost line for C is tangent to an isoquant.

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FIGURE 10-12

The Minimum Cost for a Given Level of Output

A firm that is trying to produce a given level of output, Q0, at the lowest possible cost will select the input combination at which an isocost line is tangent to the Q0 isoquant.

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FIGURE 10-13

Different Ways of Producing 1 Tonne of Grain

Countries where labour is cheap relative to capital will select labour-intensive techniques of production. Those where labour is more expensive will employ relatively more capital-intensive techniques.

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FIGURE 10-14

The Effect of a Minimum Wage Law on Employment of Skilled Labour

Unskilled labour and skilled labour are substitutes for one another in many production processes. When the price of unskilled labour rises, the slope of the isocost line rises, causing many firms to increase their employment of skilled (unionized) labour.

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FIGURE 10-15

The Long-Run Expansion

With fixed input prices r and w, bundles S, T, U, and others along the locus EE represent the least costly ways of producing the corresponding levels of output.

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FIGURE 10-16

The Long-Run Total, Average, and Marginal Cost Curves

In the long run, the firm always has the option of ceasing operations and ridding itself of all its inputs. This means that the long-run total cost curve (top panel) will always pass through the origin. The long-run average and long-run marginal cost curves (bottom panel) are derived from the long-run total cost curves in a manner completely analogous to the short-run case.

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FIGURE 10-17

The LTC, LMC, and LAC Curves with Constant Returns to Scale

(a) With constant returns, long-run total cost is strictly proportional to output. (b) Long-run marginal cost is constant and equal to long-run average cost.

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FIGURE 10-18

The LTC, LAC, and LMC Curves for a Production Process with Decreasing Returns to Scale

Under decreasing returns, output grows less than in proportion to the growth in inputs, which means that total cost grows more than in proportion to growth in output.

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FIGURE 10-19

The LTC, LAC, and LMC Curves for a Production Process with Increasing Returns to Scale

With increasing returns, the large-scale firm has lower average and marginal costs than the smaller-scale firm.

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FIGURE 10-20

LAC Curves Characteristic of Highly Concentrated Industrial Structures

(a) LAC curves that slope continuously downwards generate natural monopolies. Unit costs are lowest when one firm serves the market. (b) U-shaped LAC curves with minima at a substantial share of total market output generate markets served by a few firms.

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FIGURE 10-21

LAC Curves Characteristic of Unconcentrated Industry Structures

For survival in any market, a firm must have the lowest possible unit costs. If the minimum point of a U-shaped LAC (Q0 in a) occurs at a small fraction of market output, or if LAC is everywhere flat or rising (b and c, respectively), then small size and survival are compatible.

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FIGURE 10-22

The Family of Cost Curves Associated with a U-Shaped LAC

The LAC curve is the “outer envelope” of the SAC curves. LMC = SMC at theQ value for which the SAC is tangent to the LAC. At the minimum point on the LAC, LMC = SMC = SAC = LAC. All marginal cost curves, short run and long run, intersect their corresponding average cost curves at their minimum points.

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PROBLEM 1

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ANSWER 10-1

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ANSWER 10-5

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ANSWER 10-6

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ANSWER 10-7