1. Isoquants and Isocosts
Appendix to Chapter 7
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2. Isoquants
An isoquant is a graph that shows all the combinations of capital and labour that can be used to produce a given amount of output.
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3. Properties of Isoquant Maps
There are an infinite number of combinations of labour and capital that can produce each level of output.
Every point lies on some isoquant.
The slope of an isoquant is equal to: MPlabour / MPcapital = - MPL / MPK = ΔK / ΔL
The slope of the isoquant is called the marginal rate of technical substitution which can be defined as the rate at which a firm can substitute capital for labour and hold output constant.
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4. Isoquants Showing All Combinations of Capital and Labour That Can Be Used to Produce 50, 100, and 150 Units of Output (Figure 7A.1)
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5. The Slope of an Isoquant Is Equal to the Ratio of MPL to MPK (Figure 7A.2)
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6. Isocosts
An isocost is a graph that shows all the combinations of capital and labour available for a given cost.
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7. Isocost Lines Showing the Combinations of Capital and Labour Available for $5, $6, and $7 (Figure 7A.3)
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8. Isocost Line Showing All Combinations of Capital and Labour Available for $25 (Figure 7A.4)
The slope of an isocost line is equal to - PL / PK.
The simple way to draw an isocost is to calculate the endpoints on the line and connect them.
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9. The Cost Minimizing Equilibrium Condition
Slope of isoquant = - MPL / MPK
Slope of isocost = - PL / PK
For cost minimization we set these equal and rearrange to obtain:
MPL / PL = MPK / PK
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10. Finding the Least-Cost Combination of Capital and Labour to Produce 50 Units of Output (Figure 7A.5)
Profit-maximizing firms will minimize costs by producing their chosen level of output with the technology represented by the point at which the isoquant is tangent to an isocost line.
Point A on this diagram
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11. Minimizing Cost of Production for qx = 50, qx = 100, and qx = 150 (Figure 7A.6)
Plotting a series of cost- minimizing combinations of inputs - shown here as A, B and C - enables us to derive a cost curve.
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12. A Cost Curve Showing the Minimum Cost of Producing Each Level of Output (Figure 7A.7)
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13. Review Terms & Concepts
isocost line
isoquant
marginal rate of technical substitution
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