COST OF PRODUCTION

1. Costs Analysis are important for:a) determining the profit maximizing level of output

(MC = MR). Marginal analysis

b)determining whether to stay or shut down or operate (Price < AVC)

c) helpful in the task of finding lower cost methods to produce goods and services

2. a)Fixed Costs are costs which do not vary with level of output (p. 284).

e.g. 750bhp Equipment cost; Insurance premium; depreciation cost.

Fixed costs do not affect the production decisions or the level of output. They, however, do affect profits

b) Variable Costs are costs which vary with the level of output- these costs must be covered in order for the firm to stay in business at all times

CostsOutput Fixed Variable Total$0 $1,000,000 $0 1,000,000 1000 1,000,000 500,500 1,500,5002000 1,000,000 1,001,000 2,001,5003000 1,000,000 1,501,500 2,501,5004000 1,000,000 2,002,000 3,002,0005000 1,000,000 2,502,500 3,502,500

Notice: TFC=TC when Q=0

3a)Explicit Costs (accounting costs) are direct cash payments for hired resources. Rent, labor cost, tuition, book costs.

b)Implicit Costs reflect the value of the inputs owned and used by the owner operator; e.g. salary of an entrepreneur, or investment of savings into business (interest income foregone)

c) Economic Costs = Explicit Costs +

Implicit Costs

d)Accounting Costs are explicit costs (historical costs rather than replacement costs).

Note: It the replacement cost that is relevant in making business decsions

e)Incremental Cost is the total change in costs from implementing a particular management decision (e. g, new product line, a new advertising campaign).

f) Sunk Costs are the costs that are unrecoverable (not affected by the production decision)

Initial cost of chips =$750,000; New cost of chips =$600,000 Sunk cost =$150,000 .

4. Short-run Total Costs (p.283)a)Total Fixed Costs (TFC) are costs which do not vary with level of output.

These costs do not affect the production decision (interest payments on capital, rental expenditures on leased plant and equipment, property taxes) affect profits

Short-Run Total Costs

b)Total Variable Costs are costs which vary with the level of output.

Firm production decisions are affected by variable costs.

c)Total Cost = TFC + TVC Graph p. 283

Q TVC TFC TC AFC AVC ATC MC 0 $0 $150 150 - - - - 6 50 150 200 25.00 $8.33 33.33 $8.3316 100 150 250 9.38 6.25 15.63 5.0029 150 150 300 5.17 5.17 10.34 3.8544 200 150 350 3.41 4.55 7.95 3.3355 250 150 400 2.73 4.55 7.27 4.5560 300 150 450 2.50 5.00 7.50 10.0062 350 150 500 2.42 5.65 8.07 25.00

11

Costs

Q

150

0

TFC

TC

TVCTFC

5. Short-run Per Unit Costs Table (p. 284) and Curves (page 285)

a)AFC = TFC/Q affect profits

b)AVC = TVC/Q – per unit variable cost

AVC helps to determine whether a firm should stay (Price >AVC) in business, or go out of business

(P < AVC)when compared with product price .

c)ATC = TC/Q = AFC + AVC

This cost information is used to determine whether a company realizes profit or incurs economic losses when compared with the product price a company produces.

Price - ATC = per unit profit/loss(Price - ATC) Q = total profit/loss

d)MC = TC/ Q= TVC/ QThe additional cost of producing an additional of output.

The MC information is used to determine the profit maximizing level of output when compared with the marginal revenue (MR) .

MR = MC yields the profit maximizing level of output or loss minimizing level of output . Graph

15

Graph of Short-run Per unit Curves

Per unit costs

0 QQ

AFC

MCATC

AVC

6. The U-shape of the Short-Run per unit cost curves is explained by the law of diminishing returns (p. 285).

7. The per unit costs (AVC and MC) are inversely related to the per unit products (AP and MP).

AVCL = TVCL/Q = w*L/Q = w/ (Q/L) = w/AP

AVC = w/AP

MC = TVC/ Q = (w * L)/ Q = ( W* L)/ Q

MC = w/( Q/ L) = W/MP MC =W/MP

18

Costs

AP,MP

0

0 Q1 Q2

Output (Q)

Labor

MCAVC

MP

AP

8 a)The firm’s long-run total cost (LTC) is derived from the firm’s expansion path and shows the minimum long-run total costs of producing various levels of output.

In the LR, cost containment is important for the survival of a company (US Airways)

Long-Run costs are used for investment decisions (p. 286)

Long-run average (LAC) is most widely used for planning purpose.

b)Derivation of LAC. Illustrate

c)The LAC curve shows the lowest average cost of producing each level of output when the firm can build the most appropriate plant size (page 286).

A firm can build plant (factory) of any size in the long-run (Assume only 3 sizes: Small, Medium, or Large Size)

d)The LAC is referred to as a planning curve because the firm can build the plant that minimizes the cost of producing some desired level of output in the long-run.

LAC = LTC/Q: Graphical Derivation

9. The LAC curve is U-shaped due to: a) economies scale and b) diseconomies of scale.

10. a)Economies of scale refer to reductions in per unit costs as the rate output for a product, plant, or firm increases( due to internal, learning curve, external)

b)Diseconomies of scale refer to increases in per unit costs as the scale of operation increases. How do companies deal the problems of size? See p. 292

11 a. Sources of economies of scale:

Specialization and division of labor.Technological factors-learning curve Use of time saving devices. The spreading of advertising costsFinancial Factors (lower interest rates with size)

Quantity discounts

b. Sources of Diseconomies of scale:

The inefficiencies of managing large-scale operations

The increased transportation costs which result from concentrating in few very large factories

Exist when the cost of producing two (or more) goodsjointly is less than the cost of producing each one alone.

Formula: C(Q1) + C(Q2) - C(Q1+ Q2)

C(Q1+ Q2)

Example: Given C(Q1) =$11,000; C(Q2)= $24,000; C(Q1, Q2)= $30,000. Find S and interpret its meaning.

S= ?

S=

Comment: In the real world, economies of scale are realized with the first few output level and the LAC stays nearly flat.

Exception: Natural monopolies since the LAC curve continues to decline as output increases.

12 a)The Learning Curve shows average cost reductions over time due to production experience (ship-building, air-crafts, construction).

See pp. 288-289 in the text

b)The learning curve equation can be expressed as(288-289)

C = aQb (1)

C

Q10

C1

30

C = aQC = aQbbC2

C = aQb

C = average cost of the Qth output a = average cost of the first unit of output

b < 0 is the slope of the learning curve Q = Total output

To estimate the learning curve equation, we have to transform it as:

ln C = ln a + b ln Q

LR= (C2/C1) X 100 For instance, if the LR= 87%, it means that the

firm can reduce costs by 13% ( =1 - .87) through production experience

Given the log the Learning equation = ln C= 8.12 -. 214ln Q, find the LR at: Q1= 100 ln C= 8.12- .214ln(100)=> 7.1445

C1=>$1254.50

Q2= 200ln C=8.12- .214ln(200) =>6.9862 C2=>$1081.50 LR=(C2/C1)*100%= 86.2%

This means that the firm will reduce its unit cost by13.8% due to learning

c)Applications: airlines, appliances, ship-building, refined petroleum products.

d) Use (helps to forecast costs)Pricing of calculators at TI)

TI estimates AC reductions from learning

Sets its price below the competitor’s price and gain market share

e) Foreign sourcing of inputs including parts and skilled labor is very essential for global competition.

NSF predicts that there was a shortage of 675,000 scientists by year 2006.

13. Cost-Volume-Profit Analysis and Operating Leverage

(CVP & Break-Even Analysis)

pp. 317-327.

a) CVP examines the relationship among TR, TC, and profits of the firm at various levels of output.

b) CVP is used to determine the sales volume required for a firm to break-even and the total profits or losses at other sales levels.

14. a) QB = TFC/(P - AVC)

Given: TFC = $200; price = $10, AVC = 5

QB = 200/(10-5) = 40

b) Quantity (QT) at which target profit can be achieved:

QT = [TFC + T]/ (P - AVC)

Given: TFC =$600, T = $200, P = $30; AVC = $20

QT = (600 + 200) / (30 - 20) = 800/10 = 80

c) Target profit

( T) = QT (P - AVC) - TFC

=80 ($10) - $600 =$200

Limitations of break-even analysis are constant price and AVC.

15a) Operating Leverage refers to the ratio of the firm’s TFC to TVC.

The higher the ratio, the more leveraged a company becomes.

OL= TFC/TVC >1, highly leveraged and risky

b) It means that a company has to produce more in order to break-even.

c) Degree of operating leverage (DOL) is the percentage change of the firm’s profits divided by the percentage change in output or sales.

DOL = % /% Q = ( / Q) * (Q/)

= Q (P - AVC)/[Q (P - AVC) – TFC]

See page 325 for the interpretation of DOL value

Refers to the variability or uncertainty of a firm’s EBIT(Earnings before interest and taxes)

While business risk can be measured by a number of other factors, DOL is a measure of how sensitive a firm’s EBIT is to a given % changes in sales

The larger the DOL, the greater the degree of business risk.

Examples: Public Utilities and transportation companies

Note: The DOL increases as the firm becomes highly leveraged or capital intensive.

The firm then faces higher business risk.

Sometimes the assumptions do not hold1.Costs may be semi-variable2.Many times firms sell multiple products or

small, medium, and large varieties3.There is uncertainty as to the P, V, and F

in the problem4.The planning horizon may be longer than a

year

16. Empirical Cost Estimation

C = f(Q, quality of inputs, tech., weather)

See class exercise