Chapter 6

Supply:Cost Side of Market

Recall: TP Curve - Total Product

Slope of TP curve: MP - Marginal Product

The marginal product of an input is the additional quantity of output that is produced by using one more unit of that input.

Marginal Product of Labor Curve

Key Points of TP

TP first increases then max out and starts to decrease

TP increases at a slower pace TP is maximized when MP=0 MP is decreasing but positive when TP i

s increasing MP is decreasing and negative when T

P is decreasing MP = 0 when TP is maximized

Diminishing Returns to an Input (diminishing marginal product)

diminishing returns to an input: an increase in the quantity of an input leads to a decline in the marginal product of that input, holding the levels of all other inputs fixed

Other things held constant, as more of a variable input is used in production, its marginal productivity will decline after a certain point.

Total Product, Marginal Product, and the Fixed Input

Short-Run Production:some inputs are fixed

Total Product: Q = f (L, K, N, E) Total Product of Labor:

Q = f (L) (K, N, E fixed) Marginal Product of Labor:

MPL= dQ / dL

Average Product of labor: APL=Q/L

Short-Run Production:Q, AP, MP, and shift in Q

L \ K 1 2 3 4 5 1 25 52 74 90 100 2 55 112 162 198 224

3 83 170 247 303 342

4 108 220 325 400 453

5 125 258 390 478 543

6 137 286 425 523 598

K=1

L TP=Q MP AP

1 25 25 25

2 55 30 22.5

3 83 28 27.7

4 108 25 27

5 125 17 25

6 137 12 22.8

Homework 3

Use a table to show TP, MP, AP of labor when K=2

Use tables to show TP, MP, AP of capital when L=1, L=2, respectively

Draw the TP curves of labor when K=1, K=2, respectively

Draw the TP curves of capital when L=1, L=2, respectively

Bonus: what can you conclude from the tables and graphs?

Production: one input

TP = Q = f(L,K,N,E) When K,N,E fixed: SR TP(L) = f (L) AP(L) = TP(L) / L MP(L) = dTP(L) /dL MP is the slope of TP TP maximized when MP = 0

Short-Run Production (one input) Summary

L=0 leads to Q=0 when MP is increasing, Q is increasing

at an increasing rate when MP is decreasing, Q may still

increase but at a decreasing rate When MP=0, Q stop increasing and

start decreasing (Q is maximized). AP reaches its maximum when AP=MP

Q

L0

TP

AP

MP

E

A B

Ⅰ Ⅱ Ⅲ

FMP>APAP

MP<APAP

MP<0TP

MP=AP

AP Max

MP=0

TP Max

Questions to Consider

Why will MP decline before AP declines? Why will AP decline before TP declines? Why will MP intersect AP at AP’s maxim

um?

From Production to Cost

Production: transferring inputs into outputs Inputs: resources, production factors, - L, K, N, E Variable inputs:

– level of usage change with level of production– An input whose quantity can be altered in the short run

Fixed inputs: – level of usage does not change with level of production (in th

e Short-Run)– An input whose quantity cannot be altered in the short run

Long-run: all inputs are variable (no fixed inputs)

Costs: expenses on inputs

The total cost of producing a given quantity of output is the sum of the fixed cost and the variable cost of producing that quantity of output.

TC=TFC + TVC

SR Costs: TFC and TVC

TFC: – total amount paid for fixed inputs. – The sum of all payments made to a firm’s fixed inp

uts– not vary with output in the SR

TVC: – total amount paid to variable inputs– The sum of all payments made to the firms variabl

e inputs – increases when output increases

SR Costs: Marginal Cost

The cost of producing one additional unit of output

MC=dTC/dQIn SR, dTC = dTVC, therefore S

MC = dTVC/dQ

Increasing Marginal Cost

Increasing Marginal Cost: as more of a product is produced, the additional cost of producing one more unit of output is increasing.

Fixed, Variable, and Total Costs

0 0 40 0 40

1 80 40 12 52

2 200 40 24 64

3 260 40 36 76

4 300 40 48 88

5 330 40 60 100

6 350 40 72 112

7 362 40 84 124

Employeesper day

Bottlesper day

Fixed cost($/day)

Variable cost($/day)

Total cost($/day)

Marginal cost($/bottle)

0.15

0.10

0.20

0.30

0.40

0.60

1.00

Table 6.2, P.173

Total Cost Curve

The total cost curve shows the relationship between production level (quantity of output produced) and the total cost of the production.

It becomes steeper as more output is produced due to diminishing returns to inputs, or due to increasing marginal cost.

Total Cost Curve for George and Martha’s Farm

Total Cost and Marginal Cost Curves for Ben’s Boots

Average Cost

Average total cost, often referred to simply as average cost, is total cost divided by quantity of output produced.

Average fixed cost is the fixed cost per unit of output (total fixed cost divided by quantity of output produced).

Average variable cost is the variable cost per unit of output (total variable cost divided by quantity of output produced).

SR Costs: Average Costs

Average Fixed Cost:

AFC=TFC/Q Average Variable Cost:

AVC=TVC/Q Average Total Cost: ATC=TC/Q=(TFC+

TVC)/Q

=TFC/Q+TVC/Q=AFC+AVC

Example:Total Costs and Average Costs

Q TFC TVC TC AFC AVC ATC 0 6000 0 6000 ----- ----- ----- 100 6000 4000 10000 60 40 100 200 6000 6000 12000 30 30 60 300 6000 9000 15000 20 30 50 400 6000 14000 20000 15 35 50 500 6000 22000 28000 12 44 56 600 6000 34000 40000 10 56.7 66.7

Total Costs and Marginal Cost

Q TFC TVC TC dTC dQ MC 0 6000 0 6000 ----- ----- ----- 100 6000 4000 10000 4000 100 40 200 6000 6000 12000 2000 100 20 300 6000 9000 15000 3000 100 30 400 6000 14000 20000 5000 100 50 500 6000 22000 28000 8000 100 80 600 6000 34000 40000 12000 100 120

Q, TC, TVC, ATC, AVA, MC

Q TFC TVC TC ATC AVC MC

0 6000 0 6000 ----- ----- -----

100 6000 4000 10000

100 40 40

200 6000 6000 12000

60 30 20

300 6000 9000 15000

50 30 30

400 6000 14000

20000

50 35 50

500 6000 22000

28000

56 44 80

600 6000 34000

40000

66.7 56.7 120

Q TFC TVC TC ATC AVC MC

0 6000 0 6000 ----- ----- -----

100 6000 4000 10000 100 40 40

200 6000 6000 12000 60 30 20

300 6000 9000 15000 50 30 30

400 6000 14000 20000 50 35 50

500 6000 22000 28000 56 44 80

600 6000 34000 40000 66.7 56.7 120

Q, TC, TVC, ATC, AVA, MC

Homework 4

Based on the info given in the previous slide, draw the following curves:– ATC– AVC– AFC– MC

Describe the relationships between MC and ATC, AVC, respectively

Average Total Cost Curve for Ben’s Boots

The average total cost curve at Ben’s Boots is U-shaped. At low levels of output, average total cost falls because the “spreading effect” of falling average fixed cost dominates the “diminishing returns effect” of rising average variable cost. At higher levels of output, the opposite is true and average total cost rises.

Four curves together: Marginal Cost and Average Cost Curves

The Relationship Between the Average Total Cost and the Marginal Cost

Average Variable Cost and Average Total Cost

Employeesper day

0 0 0 40

1 80 12 0.150 52 0.650

2 200 24 0.120 64 0.320

3 260 36 0.138 76 0.292

4 300 48 0.160 88 0.293

5 330 60 0.182 100 0.303

6 350 72 0.206 112 0.320

7 362 84 0.232 124 0.343

Bottlesper day

Variable cost

($/day)

Average variable cost

($/unit of output)

Total cost

($/day)

Average total cost($/unit of output)

0.15

0.10

0.20

0.30

0.40

0.60

1.00

Marginal cost

($/bottle)

Table 6.4, P.176

80 200 260 300

330 350

362

Upward-sloping MCcorresponds todiminishing returns

MC = AVC & ATCat their minimumpoints

MC

Co

st (

$/b

ott

le)

0.05

Output (bottles/day)

0.100.150.200.250.300.350.400.450.500.550.600.65

ATC

AVC

The Marginal, Average Variable, and Average Total Cost Curves

More Realistic Cost Curves

Marginal cost curves do not always slope upward. The benefits of specialization of labor can lead to increasing returns at first represented by a downward-sloping marginal cost curve. Once there are enough workers to permit specialization, however, diminishing returns set in.

Short-Run Costs: Summary

at Q=0, VC=0, but FC>0 when MC is declining, ATC and AVC bo

th decline at an increasing rate when MC starts increasing, ATC and A

VC may both be decreasing but at a decreasing rate

MC intersects AVC and ATC at their minimum, respectively

Questions to Consider

Why will MC increase before AVC increases?

Why will MC increase before ATC increases?

Why will AVC increase before ATC increases?

Why will MC intersect AVC and ATC at their minimum, respectively?

Short-Run versus Long-Run Costs

In the short-run: fixed cost is completely outside the control of a firm.

In the long-run: all inputs are variable Fixed cost in SR may also be varied in L

R In the long run a firm’s fixed cost becom

es variable

The Long-Run Average Total Cost Curve

The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output.

Short-Run and Long-Run Average Total Cost Curves

Economies and Diseconomies of Scale

There are economies of scale when long-run average total cost declines as output increases.

There are diseconomies of scale when long-run average total cost increases as output increases.

There are constant returns to scale when long-run average total cost is constant as output increases.

Relations BetweenSR Costs and SR Production

Q=f (L, K), and TC=TVC+TFC=wL + rK AVC=TVC/Q=wL/AP*L=w/AP SMC=dTVC/dQ=d(wL)/dQ

=w(dL/dQ)

=w/MP