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DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 21
Dartmouth College, Department of Economics: Economics 21, Summer‘02
Dartmouth College, Department of Economics: Economics 21, Summer‘02
Dartmouth College, Department of Economics: Economics 21, Summer‘02
Topic 2: Theory of the Firm
Topic 2: Theory of the Firm
Economics 21, Summer 2002
Andreas Bentz
Based Primarily on Varian, Ch. 18-25
The Setup
The Setup
A firm
produces output y, which it can sell for price p(y)
» p(y) is the inverse market demand function
from quantities of inputs (factors): x , x , …
1 2
input cost (per unit): w , w , …
1 2
How can this firm produce?
technology
How should this firm produce?
cost minimization
How muchshould this firm produce?
profit maximization
2
© Andreas Bentz page 1
DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 21
Dartmouth College, Department of Economics: Economics 21, Summer‘02
Dartmouth College, Department of Economics: Economics 21, Summer‘02
Dartmouth College, Department of Economics: Economics 21, Summer‘02
Technology
Technology
Production
Intro: Production
Intro: Production
In our problem, the firm’s production
technology is given;
and: the technology is independent of the
market form (market structure):
in particular it has nothing to do with competition or
firm behavior.
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DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 21
Production Function
Production Function
A production function tells you how much
output (at most) you can get from given
quantities of inputs (factors).
Example (Cobb-Douglas): f(x , x ) = x a x b.
1 2 1 2
0.5 0.5
Here: x x .
1 2
5
Short-Run Production Function
Short-Run Production Function
In the short run, not all inputs can be varied: at least
one input is fixed.
Suppose input 2 is fixed at x = x : y = f(x , x )
2 2 1 2
We can still vary output by varying input 1. This is the
short-run production function.
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DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 21
Marginal Product
Marginal Product
Suppose input 2 is held constant: how does output
change as we change input 1?
The marginal product of input 1 is the partial derivative of the
production function with respect to input 1.
Example: Holding x constant at x = 2, how does u change as
2 2
we change x by a little, i.e. what is the slope of the blue line?
1
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Marginal Product, cont’d
Marginal Product, cont’d
Formally, the marginal product of input 1 of the
production function f(x1, x2) is:
+∆ − ∂
f (x x ,x ) f (x ,x ) f (x ,x )
MP = lim 1 1 2 1 2 = 1 2
1 ∆ →
x1 0 ∆ ∂
x1 x1
That is, at which rate does output increase as
this firm uses more of input 1?
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