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EC109 > Producer Theory > Flashcards

Producer Theory Flashcards

1
Q

2 input production function

A

Q = F(K, L)

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2
Q

What is the short run?

A

When at least 1 FOP is fixed - usually K is fixed and L is variable.

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3
Q

MPL =

A

Addition to output from hiring one extra worker.

dQ/dL = F’L partial derivative

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4
Q

What shows diminishing marginal returns to labour?

A

dMPL/dL < 0 I.e. Q”L < 0

Concave production function.

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5
Q

The slope of the production function in the SR =

A

MPL

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6
Q

Diminishing returns is a … concept?

A

SHORT RUN - adding more L to fixed K causes diminishing marginal returns to labour

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7
Q

Average product of labour =

A

Output per worker

APL = Q/L

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8
Q

Relationship between MPL and APL

A

MPL cuts through max of APL
When MPL > APL, APL is increasing
When MPL < APL, APL is decreasing

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9
Q

TP is max where…

A

MPL = 0

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10
Q

MPL is max where…

A

AT the inflection point of TP where dMPL/dL = 0

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11
Q

APL is max where…

A

MPL = APL

Or APL’ = 0

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12
Q

How can we use the TP function to find the APL?

A

Draw a ray from the origin to the TP curve. The slope of this ray gives the APL at that point.

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13
Q

Isoquants show

A

All combinations of K and L that produce a fixed level of output c.

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14
Q

MRTS =

A

Marginal rate of technical substitution.

MRTS = (-) MPL / MPK

The slope of the isoquant.

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15
Q

As we move down the isoquant, what happens to MRTS?

A

It decreases in absolute value

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16
Q

What is the total differential of the production function? Show how this gives us the formula for the MRTS.

A 
dQ = F'L dL + F'K dK
dQ = MPL dL + MPK dK
dQ = 0 along an isoquant 
dK/dL = - MPL / MPK 
So MRTS = the slope
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17
Q

MRTS shows…

A

How many units of K can be substituted for 1 extra unit of L keeping output constant.

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18
Q

3 differences between isoquants and indifferent curves

A
  1. Utility is ordinal, output is cardinal
  2. Doubling values on an indifference map doesn’t change preference ordering; doubling all inputs associated with each isoquant changes technologically feasible set
  3. ICs arise from utility functions = objective; isoquants from production function = constraint.
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19
Q

For a production function to be concave, we require… (2)

A
  1. Horizontal convexity - isoquants convex to origin

2. Vertical convexity - a chord between optimal points on first and last isoquant lies within the feasible set.

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20
Q

Horizontal convexity refers to…

A

Diminishing MRTS = SR concept

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21
Q

Vertical convexity refers to…

A

Returns to scale = LR concept (change both inputs)

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22
Q

A quasi-concave production function =

A
  • Horizontal convexity holds

- But no vertical convexity - chord lies outside choice set.

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23
Q

Returns to scale measures…

A

% change in output / % change in inputs.

  • how much output rises if we increase all inputs by the same proportion
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24
Q

Why is returns to scale a LR concept?

A

Because we vary all inputs = np fixed inputs

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25
Q

How do we work out the degree of homogeneity?

A

F(tK, tL) = t^k F(K, L)

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26
Q

Degree of homogeneity tells us…

A

Returns to scale.

K = 1 means CRS
K > 1 means IRS
K < 1 means DRS

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27
Q

How do we work out returns to scale from a Cobb-Douglas function ?

A

K = sum of exponents

a + b = 1 means CRS
a + b > 1 means IRS
a + b < 1 means DRS

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28
Q

If we have CRS, what is the shape of the production function?

A

LINEAR

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29
Q

If the production function is homogenous of degree K, what Is the degree of homogeneity of the MRTS?

A

K - 1

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30
Q

When we have IRS, what shape is the production function?

A

Increasing slope = CONVEX

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31
Q

When we have DRS, what shape is the production function?

A

Decreasing slope = CONCAVE

DRS = vertical convexity

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32
Q

Returns to scale vs diminishing returns

A

Returns to scale = LR concept, change K & L

Diminishing returns = SR concept, change L while K fixed

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33
Q

Can we have IRS and diminishing marginal returns?

A

YES e.g. If exponents of cobb Douglas are both 2/3

2/3 + 2/3 = 4/3 > 1 therefore IRS
But 0 < 2/3 < 1 therefore diminishing returns once we find second partial derivatives.

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34
Q

Formula for perfect substitutes isoquant

A

Q = aL + bK

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35
Q

Slope of perfect substitutes isoquants

A

MRTS = a/b - constant = isoquants are straight lines

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36
Q

With perfect substitutes isoquants, returns to scale =

A

CONSTANT returns to scale.

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37
Q

Elasticity of substitution formula.

A

% change in K/L / % change in MRTS

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38
Q

Returns to scale for cobb Douglas are…

A

Can have CRS / IRS / DRS - depends on sum of exponents

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39
Q

Cobb Douglas is linear in…

A

Logs - MRTS is just alpha / beta

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40
Q

Formula for perfect compliments

A

Q(L, K) = MIN {aL, bK}

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41
Q

MRTS and shape of isoquants for perfect compliments

A

MRTS = infinity on vertical, zero on horizontal, undefined at kink.
L shaped isoquants.

42
Q

Returns to scale for perfect compliments

A

CRS

43
Q

Technological progress causes… (2)

A
  1. The isoquant will shift downwards - can produce same output with fewer inputs.
  2. The shape of the isoquant may also change.
44
Q

Name 3 types of tech progress

A
  1. Neutral
  2. Labour saving
  3. Capital saving
45
Q

How does neutral tech progress affect isoquants?

A

Causes PARALLEL shift since shape unchanged - MPL & MPK affected equally.

46
Q

How does labour saving tech progress affect isoquants?

A

Isoquants shift inwards

MPK increases relative to MPL = MRTS decreases in absolute value = isoquants flatter.

47
Q

How does capital saving tech progress affect isoquant?

A

Isoquants shift inwards

MPL increases relative to MPK = MRTS increases in absolute value = more steep

48
Q

Economic costs =

A

Explicit + implicit costs

49
Q

Sunk costs =

A

Costs already incurred so cannot be avoided. They should not affect current decision making as already incurred.

50
Q

Isocost curves show

A

All combinations of K & L that a firm can afford to purchase given fixed input prices w & r and a total allowable cost level. TC constant along a given isocost curve.

51
Q

Slope of isocost line =

A
  • w/r - ratio of input prices.
52
Q

If w/r changes, what happens to isocost lines?

A

Pivots around the isoquant = change in slope + both intercept.

53
Q

Firms 2 step problem

A
  1. Minimise costs for a given level of output = L* and K*

2. Then choose output to maximise profit.

54
Q

What is the objective & constraint for cost minimisation?

A 
Objective = minimise TC
Constraint = output fixed at Q0
55
Q

Diagrammatically, what does cost minimisation do?

A

We shift in the isocost curve until it is tangential to the isoquant. This minimises cost given that we must produce Q0 output.

56
Q

All points on the isoquant are… but not necessarily…

A

All points are technologically efficient.

But not all are economically efficient I..e cost minimising

57
Q

Tangency condition for cost minimisation

A

Slope of isoquant = slope of isocost

MRTS = MPL / MPK = w/r

58
Q

Cost minimisation yields…

A

Conditional input demands - L* (r, w, Q0) and K* (r, w, Q0)

  • depend on output
59
Q

Min TC =

A

wL* + rK*

60
Q

What does the Lagrange multiplier for cost minimisation represent?

A

Lambda = how much the optimal value changes if we relax the constraint marginally = how much TC increases if we increase output marginally = Marginal cost

61
Q

Expansion path shows

A

The set of optimal combinations of L* and K* as we increase output and the isoquants shift out.

62
Q

The expansion path is a straight line if

A

MRTS unchanged along optimal points = parallel shifts = homothetic.

63
Q

How do we find corner solutions to cost minimisation?

A

Compare MPL/w and MPK/r.

Whichever is higher use only that input and zero of the other.

64
Q

What happens to the isocost/isoquant diagram if we change input prices?

A

Isoquant unchanged.
Isocost pivots around the isoquant = slope + both intercepts change
New optimal point for cost minimisation.

65
Q

In order for change in input prices analysis to hold, what two assumptions do we need?

A

1) K, L > 0 = interior solution

2) Isoquants are convex

66
Q

What causes a shift of the input demand curve?

A

If we increase output and shift isoquant out, the only way to reach this new isoquant is to all TC to rise = demand for labour rises at any given wage rate.

67
Q

Substitution between K and L if perfect compliments. Implication for input demand curves.

A

Zero substitution. If input price changes, no change in optimal = perfectly inelastic input demand curves.

68
Q

Substitution between K and L if perfect substitutes. Implication for input demand curves.

A

If W rises, move from all L to all K = infinite substitution

Perfect elastic input demand curve.

69
Q

Homogeneity of TC function in input prices

A

K = 1 - double input prices = double TC

70
Q

If we have CRS production function, our TC curve is…

Economies of scale?

A

LINEAR - MC = AC = a constant

No Economies / diseconomies of scale

71
Q

If we have DRS production function, our TC curve is…

Economies of scale?

A

DRS = concave production function = convex cost function
Increasing gradient of TC curve
MC is increasing and AC increasing = diseconomies of scale.

72
Q

MES where

A

MC = AC

73
Q

If we have IRS production function, our TC curve is…

Economies of scale?

A

IRS production function = convex = concave TC function
MC and AC are decreasing
Therefore Economies of scale

74
Q

If the production function is concave, the TC function is

A

Convex

75
Q

If input prices change, what happens to TC?

A

Change in input prices = pivot of isocost around isoquant = new optimal point substituting away from more expensive input. But TC may still rise .

76
Q

MIN TC Cost minimisation in the SR

A

MIN TC = wL* + r(K bar)

  • K is fixed
  • we find L* given that K must be K bar
77
Q

SR vs LR costs

A

SR costs tend to be higher than LR costs as K is fixed = we cannot reach cost minimising combination.

78
Q

Expansion path in SR

A

Horizontal line at K bar

79
Q

SR average total cost =

A

average fixed cost (rK bar) + average variable cost (wL*)

80
Q

The long run cost curve is known as an…

A

Envelope curve - it envelopes the SR cost curves as we change K bar

81
Q

Method for stage 2 of firms problem i.e. Profit max

A

Find Q* that maximises Pi*
Unconstrained maximisation - do not need Lagrangian
FOC: dPi/dQ = P - MC = 0
P = MC

82
Q

Method for firms 1 step problem

A 
Work out L* K* and Q* all at once. Plug in production function.
Pi = pF(K, L) - wL- rK
FOCs: (1) dPi/dL = 0 and (2) dPi/dK = 0
Use (1) to find expansion path for K
Then plug into (2)
83
Q

The firms one step problem yields…

A

Unconditional factor demands L* (p, r, w) and K* (p, r, w)

Do NOT depend on Q.

84
Q

The supply and profit functions from one step problem

A 
Q* = F(K*, L*)
Pi* = pQ* - wL* - rK*
85
Q

How do we know whether to use the 2 step or 1 step problem?

A

2 step if Q asks for conditional factor demands

1 step if Q asks for unconditional factor demands / supply function

86
Q

Profit is zero when… (2)

A 
TR = TC
AR = AC
87
Q

Profit is increasing in…

A

Price

88
Q

Profit is decreasing in…

A

r and w (input prices)

89
Q

Pi(r, w, p) is homogeneous of degree…

A

1 in p, w, r.

90
Q

Isoprofit curves show

A

All combinations of output and inputs (with p, r, w fixed) that generate the same level of profit.

91
Q

To find isoprofit curves, do we use 1 or 2 step problem?

A

use 1 step as we get unconditional input demands

92
Q

What is on axes for isoprofit curves?

A

Y axis = output (Q)

X axis = L=K or just L & assume K fixed

93
Q

Formula for isoprofit lines

A

Pi = pQ - wL - r(K Bar)
rearrange to give
Q = Pi/p + (w/p) L + (r/p) K bar

94
Q

Slope of isoprofit lines if we have L on X axis and assume K fixed

A

Slope = w/p

95
Q

Tangency condition based on isoprofit diagram

A

Slope of isoprofit = slope of production function with just labour
W/p = MPL
W = p MPL
- Extra revenue from 1 more worker = cost of this worker

96
Q

P MPL =

A

The marginal revenue product of labour

97
Q

If we change L, by how much should we change Q so that we remain on the same isoprofit line?

A

Change in Q = MPL change in L.

98
Q

A firm’s LR supply curve =

A

LRMC curve above LRAC curve

99
Q

A firm’s supply curve in the SR =

A

MC curve above AVC

100
Q

Shutdown condition in SR

A

Shutdown if AR (P) < AVC

101
Q

Shape of supply curve depends on (2)

A

Shape of MC - SR or LR?

Whether there are fixed costs.

102
Q

How does the LR supply curve compare to the SR supply curve?

A

LR supply curve is flatter than the SR supply curve (due to K bar in SR)

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