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A Closer Look at Production and Costs

CHAPTER

7 Appendix

© 2003 South-Western/Thomson Learning

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The Production Function and Efficiency

The way in which resources can be combined to produce output can be summarized by a firm’s production function

The production function identifies the maximum quantities of a particular good or service that can be produced per time period with various combinations of resources, for a given level of technology

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Properties of Isoquants

There is a different isoquant for every output rate the firm could possibly produce with isoquants farther from the origin indicating higher rates of output

Along a given isoquant, the quantity of labor employed is inversely related to the quantity of capital employed isoquants have negative slopes

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Properties of Isoquants

Isoquants do not intersect. Since each isoquant refers to a specific rate of output, an intersection would indicate that the same combination of resources could, with equal efficiency, produce two different amounts of output

Isoquants are usually convex to the origin any isoquant gets flatter as we move down along the curve

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Marginal Rate of Technical Substitution

The absolute value of the slope of the isoquant is the marginal rate of technical substitution, MRTS, between two resources

Thus, the MRTS is the rate at which labor substitutes for capital without affecting output when much capital and little labor are used, the marginal productivity of labor is relatively great and the marginal productivity of capital relatively small one unit of labor will substitute for a relatively large amount of capital

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Marginal Rate of Technical Substitution

The extent to which one input substitutes for another is directly linked to the marginal productivity of each input

For example, between points a and b, 1 unit of labor replaces 2 units of capital, yet output remains constant labor’s marginal product, MPL – the additional output resulting from an additional unit of labor – must be twice as large as capital’s marginal product, MPC

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Marginal Rate of Technical Substitution

Anywhere along the isoquant, the marginal rate of technical substitution of labor for capital equals the marginal product of labor divided by the marginal product of capital, which also equals the absolute value of the slope of the isoquant

MRTS = MPL / MPC

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Marginal Rate of Technical Substitution

If labor and capital were perfect substitutes in production, the rate at which labor substituted for capital would remain fixed along the isoquant the isoquant would be a downward sloping straight lineSummary

Isoquants farther from the origin represent higher rates of outputIsoquants slope downwardIsoquants never intersectIsoquants are bowed toward the origin

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Isocost Lines

We now turn to the combination of resources that should be employed to minimize the cost of producing a given rate of output

Suppose a unit of labor costs the firm $1,500 per month, and a unit of capital costs $2,500 TC = (w x L) + (r X C)

TC = $1,500L + $2,500C

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Isocost Lines

At the point where the isocost line meets the vertical axis, the quantity of capital that can be purchased equals the total cost divided by the monthly cost of a unit of capital TC / r

Where the isocost line meets the horizontal axis, the quantity of labor that can be purchased equals the total cost divided by the monthly cost of a unit of labor TC / w

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Isocost Line

The slope of the isocost line is given bySlope of isocost line = -(TC/r)/(TC/w) = -w/r

Thus, in our example, the absolute value of the slope of the isocost line is w /r = 1,500 / 2,500 = 0.6 the monthly wage is 0.6, or six tenths of the monthly cost of a unit of capital hiring one more unit of labor, without incurring any additional cost, the firm must employ 0.6 fewer units of capital

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Choice of Input Combinations

The profit maximizing firm wants to produce its chosen output at the minimum cost it tries to find the isoquant closest to the origin that still touches the isoquant

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Expansion Path

If we imagine a set of isoquants representing each possible rate of output, and given the relative cost of resources, we can then draw isocost lines to determine the optimal combination of resources for producing each rate of output

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Expansion PathIf the relative prices of resources change, the least-cost resource combination will also change the firm’s expansion path will change

For example, if the price of labor increases, capital becomes relatively less expensive the efficient production of any given rate of output will therefore call for less labor and more capital