Tsinghua Micro Ch21 Cost Curves课件
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Tsinghua Micro Ch21 Cost Curves(清华 李稻葵)
output level. Let cv(y) be the variable cost function. Then the total cost function is
c (y ) F c v (y ) .
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5
$
c (y ) F c v (y )
F
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c(y) cv(y)
F y6
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11
Marginal and Variable Cost Functions
Note:
MC(y)cv(y) y
y
cv(y)M C(z)dz.
0
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12
Marginal and Variable Cost Functions
$/output unit
y
Hale Waihona Puke cv(y) MC(z)dz
0
Therefore,
AVC(
y)
0
y
as
M C(y) cv(y)AVC(y). y
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14
$/output unit
M C (y )A V C (y ) A V C (y )0 y
The short-run MC curve intersects
the short-run AVC curve from below at the AVC curve’s
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3
From last Chapter: Short-Run & Long-
Run Total Costs
y Short-run
x2
output
Long-run costs are:
y expansion
c (y ) F c v (y ) .
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5
$
c (y ) F c v (y )
F
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c(y) cv(y)
F y6
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11
Marginal and Variable Cost Functions
Note:
MC(y)cv(y) y
y
cv(y)M C(z)dz.
0
精选PPT
12
Marginal and Variable Cost Functions
$/output unit
y
Hale Waihona Puke cv(y) MC(z)dz
0
Therefore,
AVC(
y)
0
y
as
M C(y) cv(y)AVC(y). y
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14
$/output unit
M C (y )A V C (y ) A V C (y )0 y
The short-run MC curve intersects
the short-run AVC curve from below at the AVC curve’s
精选PPT
3
From last Chapter: Short-Run & Long-
Run Total Costs
y Short-run
x2
output
Long-run costs are:
y expansion
《微观经济学》清华大学-Tsinghua Micro Ch14 021025.ppt
Only in one special circumstance do these three measures coincide.
$ Equivalent Utility Gains
Suppose rice can be bought only in lumps of one kilogram.
Consumer’s Surplus
p1 p1(x1), the inverse ordinary demand curve for commodity 1
Q: What is the most you would pay to enter the market?
Monetary Measures of Gains-toTrade
A: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market.
Use r1 to denote the most a single consumer would pay for a 1st kilogram -- call this her reservation price for the 1st kilogram.
r1 is the dollar equivalent of the marginal utility of the 1st kilogram.
so, as an approximation, the reservation-price curve is replaced with the consumer’s ordinary demand curve.
Consumer’s Surplus
$ Equivalent Utility Gains
Suppose rice can be bought only in lumps of one kilogram.
Consumer’s Surplus
p1 p1(x1), the inverse ordinary demand curve for commodity 1
Q: What is the most you would pay to enter the market?
Monetary Measures of Gains-toTrade
A: You would pay up to the dollar value of the gains-to-trade you would enjoy once in the market.
Use r1 to denote the most a single consumer would pay for a 1st kilogram -- call this her reservation price for the 1st kilogram.
r1 is the dollar equivalent of the marginal utility of the 1st kilogram.
so, as an approximation, the reservation-price curve is replaced with the consumer’s ordinary demand curve.
Consumer’s Surplus
Microeconomics PPT (12)
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Inputs and Output
The long run is the time period in which all inputs can be varied. The short run is the time period in which at least one input is fixed. The total product curve shows how the quantity of output depends on the quantity of the variable input, for a given quantity of the fixed input.
The total cost curve becomes steeper as more output is produced due to diminishing returns.
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Total Cost Curve for George and Martha’s Farm
Cost
Here, the first worker employed generates an increase in output of 19 bushels, the second worker generates an increase of 17 bushels, and so on…
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Diminishing Returns to an Input
There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input. The following marginal product of labor curve illustrates this concept clearly…
《微观经济学microeconomics》英文版全套课件(101页)
X RL {x R : xl 0 for l 1,..., L}
The economic constraint:
px p1x1 ... pL xL w
The Walrasian budget set (Definition 2.D.1)
Bp,w {x RL : px w}
or
u(x* ) xl
pl
px w
Solution: Walrasian demand function x*( p, w)
Utility Maximization -- Example
Example 3.D.1: the transformed Cobb-Douglas Utility Function
Expenditure Function
Expenditure function e( p,u) Min px s.t. u(x) u {x}
Properties: 1. Homogeneous of degree of one in p 2. Strictly increasing in u and nondecreasing in p 3. Concave in p 4. Continuous in p and u
Comparative Statics – Wealth Effects
The consumer’s Engel function x( p, w)
The wealth effect xl ( p, w) / w or Dwx( p, w) Normal goods and inferior goods
A choice rule C(B) B
The weak axiom of revealed preference (WARP): if x is revealed at least as good as y, then y cannot be revealed preferred to x
The economic constraint:
px p1x1 ... pL xL w
The Walrasian budget set (Definition 2.D.1)
Bp,w {x RL : px w}
or
u(x* ) xl
pl
px w
Solution: Walrasian demand function x*( p, w)
Utility Maximization -- Example
Example 3.D.1: the transformed Cobb-Douglas Utility Function
Expenditure Function
Expenditure function e( p,u) Min px s.t. u(x) u {x}
Properties: 1. Homogeneous of degree of one in p 2. Strictly increasing in u and nondecreasing in p 3. Concave in p 4. Continuous in p and u
Comparative Statics – Wealth Effects
The consumer’s Engel function x( p, w)
The wealth effect xl ( p, w) / w or Dwx( p, w) Normal goods and inferior goods
A choice rule C(B) B
The weak axiom of revealed preference (WARP): if x is revealed at least as good as y, then y cannot be revealed preferred to x
Tsinghua Micro Ch21 Cost Curves(清华 李稻葵)
$/output unit
MCs(y;x2) ACs(y;x2)
x 2 x 2 x 2
Short-run costs are:
c s ( y ) c( y ) cs ( y ) c( y ) cs ( y ) c( y )
x1 x1 x1
x1
Fixed, Variable & Total Cost Functions
Short-Run & Long-Run Total Cost Curves
The
firm has three short-run total cost curves. In the long-run, how does the firm choose amongst these three?
AVC(y)
y
MC and ATC are similarly related
Similarly, since
c( y ) ATC( y ) , y
ATC( y ) y MC( y ) 1 c( y ) . 2 y y
Therefore,
ATC( y ) 0 as y
1. Let MP1 be the marginal physical productivity of the variable input 1; 2. So the firm’s extra cost from producing one extra unit of output is w1 MC . MP1 3. This is the slope of the firm’s total cost curve. 4. If input 2 is a complement to input 1 then MP1 is higher for higher x2. Hence, MC is lower for higher x .
Microeconomics PPT (13)
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Two Necessary Conditions for Perfect Competition 1) For an industry to be perfectly competitive, it must contain many producers, none of whom have a large market share.
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►ECONOMICS IN ACTION
The Pain of Competition Sometimes it is possible to see an industry become perfectly competitive.
In the case of pharmaceuticals, the conditions for perfect competition are often met as soon as the patent on a popular drug expires. The field is then open for other companies to sell their own versions of the drug—marketed as “generics” and sold under the medical name of the drug. Generics are standardized products, much like aspirin, and are often sold by many producers. The shift to perfect competition is accompanied by a sharp fall in market price.
Tsinghua Micro Ch20 Cost Minimization(清华 李稻葵)
A Cobb-Douglas Example of Cost Minimization
(a) combined wit 1 , w 2 , y ), x* ( w 1 , w 2 , y ) 1 2
w 2/ 3 2w 1/ 3 1 2 y, y . 2w 1 w2
Conditional Input Demand Curves
x2
Fixed w1 and w2.
y y
y
x1
Conditional Input Demand Curves
x2
Fixed w1 and w2.
y
y
Cond. demand for input 2
output expansion path
Conditional Input Demands
Given
w1, w2 and y, how is the least costly input bundle located? And how is the total cost function computed?
Iso-cost Lines
x1 ( y )
x 2 ( y )
y y
y
x1
A Perfect Complements Example of Cost Minimization
The
firm’s production function is
y min{4x1 , x 2 }.
Input
prices w1 and w2 are given. What are the firm’s conditional demands for inputs 1 and 2?
Tsinghua Micro Ch21 Cost Curves(清华 李稻葵)课件-精品文档
ATC(y)
AVC(y)
AFC(y) 0 y
Marginal Cost Function
Since
the firm’s total cost function is:
c ( yF ) c ( y ) v
The
marginal cost is:
c ( y ) c ( y ) v M C ( y ) . y y
x 2 x 2 x 2 x 1 x1 x1
Short-run costs are:
cs ( y ) c( y ) cs ( y ) c( y ) cs ( y ) c( y )
x1
Fixed, Variable & Total Cost Functions
Comparing consumer behavior with producer behavior
Consumer: Maximize Utility subject to linear constraint; Producer: Minimize linear function subject to production function; Minimizing a linear function makes things much simpler; Also, the production function is cardinal; utility is ordinal !
From last Chapter: Short-Run & LongRun Total Costs
x2
y Short-run
y
y
output expansion path
AVC(y)
AFC(y) 0 y
Marginal Cost Function
Since
the firm’s total cost function is:
c ( yF ) c ( y ) v
The
marginal cost is:
c ( y ) c ( y ) v M C ( y ) . y y
x 2 x 2 x 2 x 1 x1 x1
Short-run costs are:
cs ( y ) c( y ) cs ( y ) c( y ) cs ( y ) c( y )
x1
Fixed, Variable & Total Cost Functions
Comparing consumer behavior with producer behavior
Consumer: Maximize Utility subject to linear constraint; Producer: Minimize linear function subject to production function; Minimizing a linear function makes things much simpler; Also, the production function is cardinal; utility is ordinal !
From last Chapter: Short-Run & LongRun Total Costs
x2
y Short-run
y
y
output expansion path
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Run Total Costs
y Short-run
x2
output
Long-run costs are:
y expansion
c(y)w1x1 w2x2
path
c(y)w1x1w2x2
y
c(y)w1x1w2x2
x 2
x 2 x 2
Short-run costs are:
cs(y) c(y) cs(y) c(y) cs(y) c(y)
x 1 x 1 x1
x1
Fixed, Variable & Total Cost Functions
Let F be the short-run fixed cost – F does not vary with the firm’s output level.
For y > 0, the firm’s average total cost function is
AC(y)Fcv(y) yy
AFC(y)AVC(y).
$/output unit
AFC(y) 0 as y
AFC(y)
0
y
Av. Fixed, Av. Variable & Av. Total Cost Curves
c (y ) F c v (y )
The marginal cost is:
M C (y)cv(y)c(y). y y
Marginal and Variable Cost Functions
Note:
MC(y)cv(y) y
y
cv(y)M C(z)dz.
0
Marginal and Variable Cost Functions
$
For 0 y y, choose x2 = x2. cs(y;x2)
cs(y;x2)
cs(y;x2) F
F F
0
y
y
y
$
For 0 y y, choose x2 = x2. cs(y;x2) For y y y, choose x2 = x2.
Therefore,
ATC(y)
0
y
as
MC(y) c(y)ATC(y). y
$/output unit
ATC(y)
0
as
MC(y)ATC(y)
y
MC(y)
ATC(y)
y
$/output unit
MC(y) ATC(y) AVC(y)
y
Short-Run & Long-Run Total Cost Curves
cs(y;x2)
cs(y;x2) F
F F
0
y
c(y), the firm’s longrun total cost curve.
y
y
Short-Run & Long-Run Total Cost Curves
The long-run total cost curve is the lower envelope of the short-run total cost curves.
Suppose the firm can be in one of
just three short-runs;
x2 = x2
or
x2 = x2
x2 < x2 < x2.
or
x2 = x2.
$
F =
cs(y;x2)
Fw2=x2w 2x2
A larger amount of the fixed cs(y;x2) input increases the firm’s
Short-Run & Long-Run Average Total Cost Curves
The same is true with average cost curves: The long-run av. total cost curve must be the lower envelope of all of the firm’s short-run av. total cost curves.
fixed cost.
Why does
a larger amount of
F
the fixed input reduce the
F
slope of the firm’s total cost curve?
0
y
Short-Run & Total Cost
Curves
1. Let MP1 be the marginal physical productivity of the variable input 1;
Minimizing a linear function makes things much simpler;
Also, the production function is cardinal; utility is ordinal !
From last Chapter: Short-Run & Long-
MCs(y;x2)
ACs(y;x2)
MCs(y;x2)
ACs(y;x2) ACs(y;x2)
AC(y) MCs(y;x2)
y
$/output unit
MCs(y;x2)
ACs(y;x2)
MCs(y;x2)
ACs(y;x2) ACs(y;x2)
MCs(y;x2) MC(y), the long-run marginal cost curve.
$/output unit
y
cv(y) MC(z)dz
0
MC(y)
Area is the variable
cost of making y’ units
0
y y
How is marginal cost related to average variable cost?
Since
AVC(y)cv(y), y
cs(y;x2)
cs(y;x2) F
F F
0
y
y
y
$
For 0 y y, choose x2 = x2. cs(y;x2) For y y y, choose x2 = x2.
For y y, choose x2 = x2.
Let cv(y) be the variable cost function. Then the total cost function is
c (y ) F c v (y ) .
$
c (y ) F c v (y )
F
c(y) cv(y)
F y
Av. Fixed, Av. Variable & Av. Total Cost Curves
technology is chosen to produce y? Here is an example:
$/output unit
MCs(y;x2)
ACs(y;x2)
MCs(y;x2)
ACs(y;x2) ACs(y;x2)
MCs(y;x2)
y
$/output unit
Chapter Twenty-One
Cost Curves
What do we do in this chapter?
We examine how c(y) varies with y. Why? We need to prepare ourselves for
studying firms’ supply. We have the following types of cost curves:
Short-Run & Long-Run Total Cost Curves
The firm has three short-run total cost curves.
In the long-run, how does the firm choose amongst these three?
How about the average variable cost?
It must be increasing eventually Since at least one input is fixed in
the short-run.
$/output unit Since AFC(y) 0 as y , ATC(y) AVC(y) as y
2. So the firm’s extra cost from producing one extra unit of output is
MC w1 . MP1
3. This is the slope of the firm’s total cost curve.
4. If input 2 is a complement to input 1 then MP1 is higher for higher x2. Hence, MC is lower for higher x .
$/output unit
ACs(y;x2) ACs(y;x2) ACs(y;x2)
y
$/output unit
ACs(y;x2)
ACs(y;x2)
ACs(y;x2)
The long-run av. total cost curve is the lower envelope
the short-run AVC curve from below at the AVC curve’s