chapter 12: production with multiple inputs

Question 1

2 input production plan

Answer 1

How much X is produced using labour and capital - 3 dimensional

Question 2

Long run frontiers

Answer 2

Illustrate available technology assuming all inputs can be varied

Question 3

Short run frontiers

Answer 3

Derived from long run frontiers by assuming capital is fixed and only variable is labour.

Different levels of fixed capital are different slices of the long run frontier

Question 4

Margional product of labour

Answer 4

Is the increase in output from increase in labour.
Measures as the slope on the short run frontier
As capital increases, MPL changes

Question 5

Linear slice of frontier

Answer 5

Increase in inputs by k means k-fold increase in output.

Frontier has constant returns to scale.

Question 6

Diminishing slope slice of frontier

Answer 6

Increase in inputs by k means less than k-fold increase in output.

Diminishing returns to scale.

Question 7

Slice is increasing slope.

Answer 7

Increase all inputs by k means more than k-fold increase in output.

Increasing returns to scale

Question 8

Function f is homogeneous of degree k if:

Answer 8

F(tl,tk) = t^k f(l,k)

Question 9

K > 1

Answer 9

Increasing returns to scale

Question 10

K = 1

Answer 10

Constant returns to scale

Question 11

K < 1

Answer 11

Diminishing returns to scale

Question 12

Cobb Douglas production function

Answer 12

F(l,k) = al^alpha k^beta

Question 13

Alpha + beta > 1

Answer 13

Increasing returns to scale

Question 14

Alpha + beta = 1

Answer 14

Constant returns to scale

Question 15

Alpha + beta < 1

Answer 15

Decreasing returns to scale

Question 16

Returns to scale:

Answer 16

Slices from the origin, what happens to output when all inputs increase at the same time.

Question 17

Margional product:

Answer 17

Slices that hold one input fixed.
What happens to output when one input rises all else unchanged.

Question 18

What can we have in combination

Answer 18

Diminishing margional product + increasing returns to scale

AND

Increasing returns to scale and increasing margional product.

BUT NOT

Decreasing returns tot scale and increasing margional product of one unit.

Question 19

Consumer indifference curves shows:

Answer 19

Combinations of consumption goods that produce the same level of utility.

Isoquant illustrates all input bundles that can product a given level of output without wasting any input.

Question 20

Slope of A is how many units of capital we could sub for a labour hour and maintain same production of output. This is called

Answer 20

Margional technical rate of substitution (mtrs)

Question 21

TRS =

Answer 21

• MPl / MPk

Question 22

MRS =

TRS =

Answer 22

Mrs = utility function
TRS = production function

Mrs = - (du/dx1)/(du/dx2)

TRS = -(df/dl)/(df/dk)

Question 23

Margional product of labout

Answer 23

MPl = df/dl
Change in output from a change in labour input

Question 24

MPk

Answer 24

MPk = df/dk
Change in output from a Change in capital input.

Question 25

If we assume isoquant maps are homothetic then

Answer 25

TRS is constant along any ray of the origin.

Question 26

Increase in substitutablility

Answer 26

Flatter isoquants

Question 27

Returns to scale are seen in the..

Answer 27

Rate at which isoquant labels change along rays from the origin.

Question 28

Diminishing margional product is identified by..

Answer 28

Increasing space between isoquants when one input is increased, indicating each additional unit of input yields less additional output.

Question 30

For a producer choice set to be convex,

Answer 30

any slice of the 3 dimensional set must be convex.

Question 31

A slice can be convex only if the technology has..

Answer 31

Decreasing or constant returns to scale, so all margional products are diminishing and short run production slices are convex.

Question 32

The isoquant map must have the convex it’s property..

Answer 32

For the producer choice set the be conves, means it has decreasing returns to scale and its isoquants have convex upper contour sets.

Question 33

Convex it’s of producer choice sets implies convex it’s of upper contour sets, but…

Answer 33

Convex it’s of upper contour sets does not imply convexity of producer sets.

Question 34

Consumer = Producer = For maps

Answer 34

Consumer = indifference maps Producer = isoquant maps

Question 35

For consumers, instead of Margional utility..

Answer 35

MP of input

Question 36

Vertical slices are only for

Answer 36

Producers, not consumers

Question 37

Properties of isoquants: Monotonicity

Answer 37

More is better More input = more output Higher valued isoquants

Question 38

Properties of isoquants: Convexity

Answer 38

Average > extremes Average input on some isoquant = increase output. Diminishing trs

Question 39

Properties of isoquants: Continuity

Answer 39

No sudden jumps in production

Question 40

Properties of isoquants: Completeness

Answer 40

There is always an output (X) for every input bundle (l,k)

Question 41

Properties of isoquants: Transitivity

Answer 41

Xa > Xb Xb > Xc So xa > Xc

Question 42

Economic efficiency =

Answer 42

Least cost production, maximise output.

Question 43

Isoquant: Isocosts:

Answer 43

Isoquant: technical efficiency Isocosts: analogous to budget lines

Question 44

Convex producer set =

Answer 44

Decreasing returns to scale

Question 45

When technology is homothetic

Answer 45

The economically efficient input bundles lie on the same ray from the origin.

Question 46

From the total cost curve we can derive:

Answer 46

MC and AC

Question 47

Supply curve =

Answer 47

MC above AC

Question 48

Who doesn’t have to pay attention to output prices?

Answer 48

A producer that only minimises costs. Only input prices (w,r) matter for determining the least cost way of producing different levels of output.

Question 49

Cost minimisation implies (Equation)

Answer 49

-TRS = MPl / MPk = w/r

Question 50

Profit maximisation implies: (Equation)

Answer 50

MRPl = pMPl = w MRPk = pMPk = r

Question 51

Law of diminishing margional product

Answer 51

MP of each input is initially increasing but eventually decreasing.

Question 52

Decreasing returns to scale can be represented if

Answer 52

Isoquants are with output numbers that increase at a decreasing rate along the ray from any origin

Question 53

Input prices =

Answer 53

Slope of isocost

Question 54

Isocost lines =

Answer 54

-w/r

Question 55

Profit pi =

Answer 55

Pxa- wla- rka

Question 56

Difference in short run v long run

Answer 56

Capital is not in short run, cuz firm has already committed to rent the capital regardless of output. Short run px^a - wl^a Long run px^a - wl^a - rk^a

Question 57

If horizontal slices of isoquants look normal they imply

Answer 57

Convexity of averages > extremes

Question 58

Can you see the vertical shape of frontier from the isoquant?

Answer 58

You would be able to infer the vertical shape from the rate at which isoquant change along the ray from the origin

Question 59

Increasing returns to scale means

Answer 59

Not convex

Question 61

With a homothetic frontier what can be concluded about how the cost minimising input bundles in your isoquant map can be related to one another.

Answer 61

We can say the cost minimising input bundles all lie on the same ray from the origin in the isoquant graph and -w/r = TRS holds for all input bundles if it does for one.

Question 62

For a sigmoid frontier ac + mc curves are shaped like

Answer 62

Normal u cuz increasing and decreasing returns to scale

Question 63

Cost minimising conditions hold on every isoquant so long as there is

Answer 63

Homotheticity

Question 64

If price decreases

Answer 64

Intersection of price with mc decreases so production falls so lower isoquant but same slope (wr)

Question 65

What happens to ration of capital to labout in production process

Answer 65

Remains unchanged even if decresed (l,k) cuz same proportions

Question 66

When fees increase the lowest part of the AC curve shifts..

Answer 66

Right because MC is unaffected by FC.

Question 67

Decreasing RTS does what to mc + ac

Answer 67

Increases mc and ac cuz each additional cost, costs more per thing