Chapter 18 Technology

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Chapter 18 Technology
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Inputs and outputs. Factors of production
land, labor, capital, raw materials, and
so on.
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A production set p321
Y Output
Y f (X ) production function
Production set
X Input
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Examples of technology (isoquants analysis)

• Fixed proportions,
• Perfect substitutes,
• Cobb-Douglas.
• Figs. p322

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Fixed proportion
x2
Isoquants
x1
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Perfect subsitutes
x2
Isoquants
x1
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Assumptions of technology monotonic (free
disposal),
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and convex. p324
x2
a2
(a1/2 b1/2 , a2/2 b2/2)
b2
isoquant
x1
a1
b1
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The marginal product, MPi d y / d x i . Y is
output
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The technical rate of substitution (TRS)

• With d y 0 along any isoquant,
• TRS (x1, x2 ) d x2 / d x1
• MP1 (x1, x2) / MP2 (x1, x2 ).

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The long run (LR) and the short run (SR)
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Returns to scale Increasing, decreasing, and
constant gtf ( t x ) lt t f ( x )
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Chapter 19 Profit Maximization
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The organization of firms

• Proprietorships,
• partnerships,
• corporations.

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SR profit maximization

• p py - w1x1 - w2x2
• y p/ p w2x2 / p w1x1 / p
• describes isoprofit lines,
• max x1p gives pMP1 w1.
• Fig. p337

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Profit maximization
Isoprofit lines slope w1/p
Output
y
y f (x1, x2) Production function
p/pw2x2/p
x1
x1
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Optimum lies on the tangency of an isoprofit line
and the production function.
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P324 Comparative statics

• Increasing p increases x1 and then y.
• Increasing w1 reduces x1,
• and thus the factor demand curve follows.
• LR both x1 and x2 are variable.
• Figs.

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Comparative statics
????
????
f(x1)
f(x1)
High w1
Low p
Low w1
High p
x1
x1
A
B