Principles of Economics

ProductionCosts

Deduction of supply

Production• PRODUCTION is a process in which inputs are

transformed into outputs. Outputs can be either consumed or used as an input for another production process (corn, corn flour, bread).

• PRODUCTION is organized in small, medium and large companies. Large companies have lower interest rates and attract more capital, while small companies are more adaptable to new circumstances

Total product

• PRODUCTION FUNCTION (TP or q) expresses the maximum amount of production (output) that can be produced using the given amount of inputs (K, L, A)

• q = TP(K, L, A) =B×f(K,L,A)

Marginal and average product• MARGINAL PRODUCT (MP) is a change in total

product due to an increase in the amount of inputs by 1 unit.

MPL = TP(L)-TP(L-1)

MPK = TP(K)-TP(K-1)• AVERAGE PRODUCT (AP) is the ratio of total product

and current amount of inputsAPL = TP/L

APK = TP/K• GRANIČNI proizvod je porast ukupnog proizvoda

uslijed porasta količine inputa za jednu jedinicu:

q

0 L

TP

q

0 L

MP

AP

• Vertical cut of a production function – in the short run (the other inputs are held constant)• Short run: at least one input is fixed• Long run: all inputs are variable

Vertical cut of a production function

Production elasticity

• % change of the output caused by a 1% change of the input:

AP

MP

KKqq

E KTP

,

AP

MP

LL

qq

E LTP

,

Returns

• LAW OF DIMINISHING RETURNS says that every additional unit of an input, other inputs being constant, brings each time less of the additional output (MP decreases).

• RETURNS TO A FACTOR of production observe how the output changes when a single input changes, other inputs kept constant.

• RETURNS TO SCALE observe how the output changes when all the inputs increase in the same proportion.

1 input is doubled

Output is less then doubled

Decreasing returns to a factor

Eq < 1

Output is doubled

Constant returns to a factor

Eq = 1

Output is more than doubled

Increasing returns to a factor

Eq > 1

All inputs are doubled

Output is less then doubled

Decreasing returns to scale

Eq,K + Eq,L < 1

Output is doubled

Constant returns to scale

Eq,K + Eq,L = 1

Output is more than doubled

Increasing returns scale

Eq,K + Eq,L > 1

Technological progress

• Technological progress (B) is the improvement of production processes by improvement of the old products or invention of the new ones.

• Technological progress can be either a PRODUCT INNOVATION or PROCESS INNOVATION.

• Product innovation: development of new goods• Process innovation: improvement of the production

processes• Technological progress stretches production function

upwards without additional use of inputs.

Technological progress

q

0

TP1

TP2

K, L

B↑

Isoquants

• Isoquants are a horizontal cut of a production function showing all the combinations of inputs with which one can produce the same amount of goods q.

• Slope of the isoquant is Marginal rate of technical substitution, MRTSab . It tells by how much the use of b has to increase of a decreases by 1 small unit (a and b are inputs)

q2

L

0 K

q3

q4

q1

ΔK = 1

ΔL = MRTSKL

ISOQUANTS

Isocost

• ISOCOST is a line that connects all the combinations of inputs that cause the same cost.

• Slope of the isocost equals the ratio of the input prices

TCqpqp yyxx

xy

x

yy q

p

p

p

TCq

y

0 x

TCqpqp yyxx

xy

x

yy q

p

p

p

TCq

y

x

p

p

yp

TC

xp

TC

yp

TC '

xp

TC '

TC’ > TC

The minimum cost production combination

• The minimum cost of production of certain amount of goods q* is achieved when isocost is tangent to the isoquant that corresponds to the amount of goods q*.

y

xxy p

pMRTS

y

x

y

x

p

p

MP

MP

y

xxy MP

MPMRTS

y

y

x

x

p

MP

p

MP

q2

y

0 x

q3

q1

xy

x

yy q

p

p

p

TCq

y

xxy p

pMRTS

Exercise 1• 1) Based on the values of average product of labour find total and marginal

product!

L TP AP(L) MP(L)

0 01 202 223 194 175 15

• Solution:

L TP AP(L) MP(L)

0 0 01 20 20 202 44 22 243 57 19 134 68 17 115 75 15 7

Exercise 2

• If marginal product of labour (MPL) is 10, marginal product of capital (MPK) 20, and marginal product of (MPN) 15, what are the prices of capital (PK) and land (PN) if wages (PL) are 5 and company has minimum costs?

solution

Costs• So far costs were expressed as a function of the amount

of inputs TC(q(K,L))• Now costs will be analyzed as a function of the quantity

of production TC(q)• Costs are either VARIABLE (change with the quantity of

production) or FIXED.• Average total costs (AC or ATC) are the costs per unit of

production: AC = TC/q• Average fixed costs (AFC) are fixed costs per unit of

production: AFC = AFC/q• Average variable costs (AFC) are fixed costs per unit of

production: AFC = FC/q

• TC/Q = VC/Q + FC/Q• AC = AVC + AFC• Marginal costs (MC) – increase in costs when q

increases by 1.• MC(q) = TC(q) – TC(q-1) = VC(q) – VC(q-1) • MC = ΔTC/ Δq

p

0 q

TC

p

0 q

MC

VC

AVC

AC

AFC

FC

Production and costs relation

• TC(1) = wL1 + rK1 + iA1 where L1, K1, A1 are the amounts of inputs needed to produce 1 unit of output.

• If prices of inputs (w, r, i) fall TC decrease• If technology progresses (B↑) the use of

inputs fall (L1↓, K1↓, A1↓) and TC decrease

Economies of scale• Economies of scale is a situation in

which average costs of production fall as quantity of production increases.

• Diseconomies of scale is a situation in which average costs of production fall as quantity of production increases.

• Cost elasticity: % change of costs caused by a 1% change in produced quantity

p

0 q

AC

MC

Diseconomies of scaleAC risesETC > 1

Economies of scale

AC fallsETC < 1AC

MC

qq

TCTCETC

/

/ E TC =

1

Other terms about costs

• Substitution rule: if an input becomes cheaper, it will be used more and the other inputs will be used less until MP/price of inputs becomes equal again.

• Economic costs include opportunity costs, but not sunk costs

• Accounting costs:• Profit & Loss Statement: Π = TR – TC (in a time

period)• Balance sheet: Assets = Capital + Liabilities (at

certain point of time)

Exercise 3

• If fixed costs are 100 and variable costs increase by 30 kn for each additional unit of output find all cost functions.

solution

• FC = 100• VC = 30Q• TC = FC + VC = 100 + 30Q• AFC = FC/Q = 100/Q• AVC = VC/Q = 30• AC = 100/Q + 30• MC = 30

Exercise 4

• Based on the dana in the Table find total costs (TC), average fixed costs (AFC), average variable costs (AVC), average total costs (AC) and marginal costs (MC) and then show them graphically.

Q VC

0 0

5 15000

10 25000

15 32500

20 42000

25 54500

30 71500

35 96500

solution

Q VC FC TC AFC AVC AC MC

0 0 40000 40000 - - - -

5 15000 40000 55000 8000 3000 11000 3000

10 25000 40000 65000 4000 2500 6500 2000

15 32500 40000 72500 2667 2167 4833 1500

20 42000 40000 82000 2000 2100 4100 1900

25 54500 40000 94500 1600 2180 3780 2500

30 71500 40000 111500 1333 2383 3717 3400

35 96500 40000 136500 1143 2757 3900 5000

0 5 10 15 20 25 30 35 Q

140000

120000

100000

80000

60000

40000

20000

0

FC

VC

TC

0 5 10 15 20 25 30 35 Q

10000

8000

6000

4000

2000

0 AFC

AVC

AC

MC

Exercise 5:

• Marginal costs and fixed costs are known and given in the following table. Find FC, VC, TC, AFC, AVC and AC.

OUTPUT MC VC FC TC AFC AVC AC0 801 75 802 65 803 55 804 65 805 75 806 85 807 95 80

OUTPUT MC VC FC TC AFC AVC AC0 80 801 75 75 80 155 80,0 75 155,02 65 140 80 220 40,0 70 110,03 55 195 80 275 26,6 65 91,64 65 260 80 340 20,0 67 85,05 75 335 80 415 16,0 70 83,06 85 420 80 500 13,3 73 83,37 95 515 80 595 11,4 57 85,0

Supply and profit maximization on perfectly competitive markets

• Perfect competition properties:1. Many small companies unable to affect prices

(price takers)2. Market demand is horizontal (Ed = -∞)3. Marginal revenue is equal to price since price is

constant4. Perfect information5. Homogeneous product6. Free entry and exit

p

0 q

MC

AVC

AC

•Assumption: company maximizes its profit•Profit is a difference between total revenue and total costs•TOTAL REVENUE (TR): TR = p×q•Profit maximization condition:

MR = MC•Since P = const. MR = ⟹ P = MC•It means that for for each price p supplied quantity will be determined by equation p = MC:MC

Shutdown and breakeven point

If p = AVC then only variable costs are covered. Then company has to close immediately SHUTDOWN ⟹POINT (SDP)

Π = TR – TC = p×q – AVC×q – FCΠ = q(p – AVC) – FC , p = AVC

⟹ Π = - FC • If p = AC then revenues match the costs covering both

VC and FC (Π = 0) BREAKEVEN POINT(BEP)⟹Π = p×q – AC×qΠ = q(p – AC) , p = AC

⟹ Π = 0

p

0 q

MC

AVC

ACMC

SSRBEP

Z

p

0 q

MC

AVC

ACMC

SLR

Supply in the long run (MC above AC)Supply in the short run (MC above AVC)

Profit in perfect competition

p

0 q

MC

AC

pMC

p

0 q

MC

AC

p

MC

Extra profits (short run) Normal profits (long run)

Exercise 6

• Daily output of a company earns it TR = 5000$. Company maximizes its profit. Average cost is AC = 8$, marginal cost MC = 10$ and average variable cost AVC = 5$. What is the amount of production and fixed cost FC?

solution

TR = 5000 (TR=P*Q)P = MC = 10 => Q = 500

AC = AVC + AFCAFC = 8 – 5 = 3FC = AFC*Q = 3*500 = 1500 kn

Exercise 7Company sells a good which price is p = 62 on a perfectly competitive market. Company’s average variable costs are given with the following table. Fixed costs are 168.

Find quantity at which company a) maximizes its profit, b) shuts down and c) has breakeven point

q AVC

0 -1 202 143 104 85 86 107 148 209 2810 38

solution

Short run supply: MC for q > 5, Long run supply: MC for q ≥ 7

q FC AVC VC MC TC AC0 168 - 0 - 168 -1 168 20 20 20 188 188,002 168 14 28 8 196 98,003 168 10 30 2 198 66,004 168 8 32 2 200 50,005 168 8 40 8 208 41,606 168 10 60 20 228 38,007 168 14 98 38 266 38,008 168 20 160 62 328 41,009 168 28 252 92 420 46,6710 168 38 380 128 548 54,80

Shut down point

Break even pointOptimal production level

P Q TR TC FC VC AC AVC MC suggestion5 100 100 6 5*

100 500 5* 4100 700 8 4 10

4 100 600 500 5100 100 200 6 950 500 100 300 7

Exercise 8There are 6 situations in the following table. Give the advice what to do in every situation:a) Keep the current level of output b) Increase the pricec) Increase productiond) Lower the pricee) Lower productionf) Stop production

solution

P Q TR TC TFC TVC ATC AVC MC SAVJET5 100 500 600 100 500 6 5* f5 100 500 500 100 400 5* 4 5 a7 100 700 800 400 400 8 4 10 e4 100 400 600 100 500 6 5 5 f10 100 1000 800 200 600 8 6 9 c10 50 500 400 100 300 8 6 7 c

1. P=AVC -> f Stop production!2. MC=ATC -> a Keep the current production level!3. MC>P -> e Lower production!4. P<AVC -> f Stop production!5. P>MC -> c Increase production!6. P>MC -> c Increase production!

Exercise 9

• A farmer rents 10 hectares of land and pays $5,50 per hectare. Depending on the working hours employed, farmer’s wheat production changes (Table). Wage is $5.

Q (tons of wheat) L (working hours)

0 0

1 6

2 11

3 15

4 21

5 31

6 45

a) Find TCb) Find MC, AC, FC, AFC, AVCc) Find APL and MPL

Q L VC TC MC AFC AVC AC APL MPL

0 0 0 55 - - - - - -

1 6 30 85 40 55 30 85 0,17 0,17

2 11 55 110 25 27,5 27,5 55 0,18 0,20

3 15 75 130 20 18,33 25 43,33 0,20 0,25

4 21 105 160 30 13,75 26,25 40 0,19 0,17

5 31 155 210 50 11 31 81 0,16 0,10

6 45 225 280 70 9,17 37,5 107,5 0,13 0,07

FC = 5.5×10 = 55