july24

Outline for Thursday, July 24

� Remember

� Homework due Friday

� Midterm Monday

� Technology

}Make a change for next week?� Technology for next week?

The Slutsky equation

� The marginal effect of a price change is called the elasticity of demand

� Before we used the demand curve to find it

� But now we have a deeper model of the consumer

θξεε −= *






θξεε −= *


� The total effect of the change on the quantity is the sum of…





θξεε −= *



� The substitution effect, ε*, which tells us how quantity would change along the old indifference curve

Un

its o

f g

oo

d Y

26

For any slope, gives us a point

along the indifference curve

Compensated demandCompensated demand

Compensated Demand

Un

its o

f g

oo

d

Units of good X

6 7 13

10





θξεε −= *



� The substitution effect, ε*, which tells us how quantity would change along the old indifference curve, and

� The income effect, -θξ, which tells us how quantity responds to the consumer’s shrinking budget set

Un

its o

f g

oo

d Y

h

f

g

Income effect ofthe price rise

Income and substitution effects: normal goodIncome and substitution effects: normal good

Units of Good X

Un

its o

f g

oo

d

I1

I2

I3

I4

I5

I6

Substitutioneffect

Incomeeffect

QX1

f

B2 B1

QX2QX3

B1a


� The substitution effect, ε*

� Always opposes the price change because MRS falls

� Is the elasticity of the compensated demand curve

� The income effect, -θξ

θξεε −= *







θξεε −= *


� Opposes the price change for normal goods

� P rises � I falls � X falls

� Moves with the price change for inferior goods

� P rises � I falls � X rises






θξεε −= *


� Opposes the price change for normal goods

� P rises � I falls � X falls

� Moves with the price change for inferior goods

� P rises � I falls � X rises

� If an inferior good has a strong enough income effect, it will have an upward-sloping demand curve and be Giffen: ε > 0


� Remember


� Midterm Monday

� Review Wednesday� Review Wednesday

� Technology

Production

� We’ve completed our model of the demand side

� How do suppliers choose how much to supply?

Production



� They maximize profit

Production




� For consumers, we had two pieces of their puzzle� For consumers, we had two pieces of their puzzle

� Preferences – internal factors

� The budget set – external factors

Production







� For firms, we will have the same elements

� Technology

� Prices of inputs and outputs

Production







� For firms, we will have the same elements

� Technology

� Prices of inputs and outputs

� Today we will describe the firm’s technology

The Production FunctionFig. 9.2

� How can a firm transform inputs into outputs?

Taken from a book by Robert Frank

),( LKfq =

K CapitalL Laborq Output

The Production Function

� The production function f tells us how much outputthe firm could make with the inputs L and K

Fig. 9.2


),( LKfq =

K CapitalL Laborq Output

Making software

� To make one program, we need either

� 3 techies in 1 cubicle

� 2 techs in 2 cubicles

� 1 tech in 3 cubicles� 1 tech in 3 cubicles

Making software

� To make one program, we need either

� 3 techies in 1 cubicle

� 2 techs in 2 cubicles

� 1 tech in 3 cubicles� 1 tech in 3 cubicles

� We can mix and match, taking averages

The Production FunctionFig. A.9.4



� This is a 3D function, so we can fix one variable at a time to graph it

),( LKfq =



),( LKfq =

� Fixing q = q0 gives us isoquants, where K and L can produce at most q0produce at most q0


q ≡ 8

x2Taken from a presentation onSlideshare

q ≡ 4

x1

q ≡ 6

q ≡ 2


Output, y

y ≡ 8

y ≡ 6

Taken from a presentation onSlideshare

x1

x2y ≡ 4

y ≡ 6

y ≡ 2

The Production Functionx2


x1q


x2


x1

q

The Production FunctionTaken from a presentation onSlideshare

x1

q


q


x1

q


y


x1


q


x1

The Isoquant MapFig. A.9.5


Isoquant Map for Cobb-Douglas Production

Fig. A.9.6


Isoquant Map for Perfect Complements“Fixed-proportions technology”

Fig. A.9.7




),( LKfq =




),( LKfq =


� Fixing K = K0 gives us the short-run production function

Figure 6.1 Production Relationships with Variable Labor

B

C

110

90

(a)

© 2007 Pearson Addison-Wesley. All rights reserved.

6–48

A

11640

L , Workers per day

56

The Long-Run and the Short-Runsx2

x1q

The Long-Run and the Short-Runs

x2

x1q


x2

x1

q


x2x2

x1

q


x2

x1

q


q

x2 x1

q


q

x1

q



),( LKfq =



� This is a cross-section of the production function



),( LKfq =




� In the short run, firms cannot change their capital



),( LKfq =





� Different fixed levels of capital give us different cross-sections


q

x1

q

Four short-run production functions.



),( LKfq =





� Different fixed levels of capital give us different cross-sections

�The short run is how long it takes to change K

The Production Function ),( LKfq =

� The short run curve slopes upward for productive levels of labor

� More labor produces more output




� Where it slopes downward

� There are too many workers

� There is decreasing total product of labor or decreasing returns

� The firm will never produce here








� For low levels of labor, f(K0, L) increases steeply because there is a division of labor








� For low levels of labor, f(K0, L) increases steeply because there is a division of labor

� Beyond some point, the slope of f(K0, L) slope falls. Here, we have a diminishing marginal returns or a diminishing marginal product of labor


� The slope of the short run curve f(K0, L) is called the

Marginal Product of Labor, MPL. To reiterate…

� MPL increases for low levels of input

� MPL decreases beyond some point. Diminishing MPL or diminishing marginal returns goes into effect heremarginal returns goes into effect here


� Remember


� Midterm Monday

� Review Wednesday� Review Wednesday

� Technology

� Summary

Production

� We modeled the consumer by

� Describing their preferences

� Describing how they respond to prices – maximize utility

Production

� We modeled the consumer by

� Describing their preferences

� Describing how they respond to prices – maximize utility

� We’ll model the firm by� We’ll model the firm by

� Describing their technology

� Describing how they respond to prices – maximize profits

The production function

� The firm’s technology is described by its production function

� What’s the most output, q, that can be made out of the inputs L and K?

),( LKfq =




),( LKfq =

� We can map this 3D function by holding one variable constant

� q = q0 gives us isoquants

� K = K0 gives us the short-run production function

The Isoquant MapFig. A.9.5





),( LKfq =


� As with the utility function, we know that “more makes more”. This tells us that

� Isoquants cannot cross

� Isoquants are downward-sloping




),( LKfq =


� As with the utility function, we know that “more makes more”

� Unlike the utility function, the quantity q means something, and we cannot rescale f

july24

Technology

marginal effect

price change

theelasticity of demandbefore

deeper model

demand curve

slutsky equation

consumerthe total effect