![Page 1: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/1.jpg)
Unit 6.
Analyses of SR Costs & Profits as Functions of
Output Q
![Page 2: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/2.jpg)
‘Liquid Gold’ Economics?
Recent increases in crude oil prices have prompted much interest in trying to figure out their likely consequences on fuel prices ‘at the pump’. Politicians and others often wonder if pump price increases are ‘out of line’ with actual increases in the cost of the crude oil input. Are their concerns warranted?
![Page 3: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/3.jpg)
No More Babies?
The CEO of Memorial Hospital recently conducted financial reviews of all departments in the hospital. During the review process, the head of the obstetrics unit proposed trying to increase the number of babies delivered in the department to make it more profitable. After reviewing the department’s financial statements for the previous month, the CEO discovered the unit delivered 540 babies that generated total costs of $3.132 million and total revenues of $2.754 million. The CEO raised the question as to why they would want to increase the number of deliveries when the unit was already losing $700 per delivery? How should the unit’s head respond to this concern?
![Page 4: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/4.jpg)
New Product Launch Advice
Assume Compaq is scheduled to launch next month a new server at a cost of $5,500. This server will be competing against Dell’s version that was just introduced to the market. Dell’s server has basically the same features (and even a few more) for a cost of $4,500. To date, Compaq has invested more than $2.5 million in the development of its new server. What advice would you give Compaq on launching its new server, keeping in mind all the development money the company has already invested into the product?
![Page 5: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/5.jpg)
How to Produce?
Several years ago, John Deere was about to begin building a capital-intensive factory to produce large, four-wheel-drive farm tractors. Then, grain prices dropped dramatically which reduced tractor demand. Deere management considered 1) stopping the construction of its own factory and, instead, 2) purchasing a Canadian company that could add to their tractor assembly capacity. Management recognized the company would have higher fixed costs, but lower marginal costs if it were to go ahead with construction of its own plant. Which course of action would you have recommended be pursued by Deere management?
![Page 6: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/6.jpg)
Lower Price to Sell More?
Joe is the district sales manager for Agri Green. He has five sales representatives, each with their own geographical territory, reporting directly to him. One of his reps has noted it has become increasingly difficult to compete against other products with the company’s current stance on maintaining relatively high prices by industry standards. The rep has proposed permission to cut price by 10%. With current prices, the company’s profit margin is 25%. The sales rep is confident he/she could sell 50% more product with the 10% price reduction. Should Agri Green give the sales rep permission to sell at a 10% lower price?
![Page 7: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/7.jpg)
“Gentlemen, Stop Your Engines”
Decker Truck Lines owns and operates about 600 semi tractor-trailers. Rising diesel fuel prices have been cutting into the company’s profit. Management is looking at alternative ways of reducing diesel fuel expenses. One strategy being considered is to offer drivers incentives (bonuses) to reduce idling time while out on the road. What specific information would be needed to implement such a plan and when would this plan result in increased profits for the company?
![Page 8: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/8.jpg)
Revenue/Cost Analysis
Cy Shops’ manager has provided you with the following information for the business (q = units of product sold)TR = 44q – q2
TVC = 4qTFC = 120The manager wants you to calculate the level of quantity sales that will result in the company a) breaking even, b) maximizing its profit, and c) maximizing its sales. What do you tell the manager?
![Page 9: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/9.jpg)
Costs of Production(Overview of Reality)
Production costs are determined by1) the productivity of inputs used by a
business firm and2) the prices paid for inputs used. The more productive the inputs are (i.e. the more efficient the production process is), the lower the costs of production will be. Likewise, lower input prices also result in lower costs of production.
![Page 10: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/10.jpg)
Cost Concepts
SR and LR SR fixed & variable LR variable only
Fixed and Variable Fixed don’t change
w/output Variable vary
w/output
Cash and Noncash Cash = ‘explicit’ Noncash = ‘implicit’
= ‘opportunity’
foregone= ‘lost’ income
Total & Average & Marginal
TFC, TVC, TCAFC, AVC, ATCMC
![Page 11: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/11.jpg)
Opportunity Cost Examples
Activity Opportunity Cost
Work at home Lost wages
Own & operate a business Lost wagesLost interest
Own & operate farm land Lost rentLost interest
Own & operate machinery Lost interestLost rent
Attend college Lost wages
Skip class/party Lost knowledgeLower grade
Go to class/study Lost workLost sleep
![Page 12: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/12.jpg)
Cost Concepts
1. Total = total dollar cost associated with a given q of output
2. Average = dollar cost PER UNIT OF OUTPUT
3. Marginal = ADDITIONAL COST per unit of ADDITIONAL OUTPUT= added cost of producing one more unit of output
![Page 13: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/13.jpg)
Cost Graphs
![Page 14: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/14.jpg)
Graphical Derivation of TVC from TP (L = variable input)
1. Multiply L by W to get TVC2. Rotate graph 90° counter
clockwise3. Flip graph 180°
![Page 15: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/15.jpg)
Cost Graphs (cont’d)
![Page 16: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/16.jpg)
Cost Graphs (cont’d)
![Page 17: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/17.jpg)
General Cost Equations
Cost Concept Average Total
Fixed AFC = TFC/Q TFC = AFC · Q
Variable AVC = TVC/Q TVC = AVC · Q
Total ATC = TC/Q TC = ATC · Q
![Page 18: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/18.jpg)
TFC in Avg Cost Graph
Total
![Page 19: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/19.jpg)
TVC in Avg Cost Graph
![Page 20: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/20.jpg)
TC in Avg Cost Graph
![Page 21: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/21.jpg)
Solving for TVC as function of q of output given production function
equation:
Step #1: Solve for L as a function of q given the
production function equation (i.e. solve for the inverse equation)
Step #2: In the TVC equation, TVC = wL,
substitute the L as a function of q equation for L
![Page 22: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/22.jpg)
Calculating Cost Equations from Production Info
Assume
q = 50L [L=(1/50)q = .02q]w = $20,000TFC = $1,000
Calculations
TVC = w•L(q) = w (.02q) = (20,000)(.02q) = 400q
TC = TFC + TVC = 1000 + 400q
AFC = TFC/q = 1000/q
AVC = TVC/q = 400q/q = 400
ATC = AFC + AVC= 1000/q + 400
MC = = 400
TC
q
![Page 23: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/23.jpg)
Oil Production & Cost Questions
1. If there are 44 gallons (output = Q) of oil per barrel (input = B), what is the corresponding production function equation?
2. Given the price of a barrel of oil, what is the TVC and AVC equations for producing gallons of oil, and how do these changes with changes in the price of a barrel of oil?
![Page 24: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/24.jpg)
Review of some cost & production fn concept
relationships
MCTC
Q
W L
Q
W
MPL
AVCTVC
Q
WL
Q
W
APL
q f k L SR production fn ( , )
L = f(q)
TVC=WL=wf(q)
![Page 25: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/25.jpg)
SR Profit Max (output)
= TR – TCmax /q = 0
TR/q - TC/q = 0 MR – MC = 0 MR = MC
![Page 26: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/26.jpg)
Optimal Output Level
Profit-maximizing level of output A manager should keep producing
additional output up to the point where the additional income equals the additional cost from the last unit
MR = MC
![Page 27: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/27.jpg)
NOTE: Optimal Input Level(e.g. labor)
MRP = MFC
MPL • MR = w
MR =
MR = MC
w
MPL
![Page 28: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/28.jpg)
MRP vs MR
MRP= additional revenue peradditional unit of input
MR = additional revenue peradditional unit of output
![Page 29: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/29.jpg)
MFC vs MC
MFC= additional cost peradditional unit of input(= marginal factor cost)
MC = additional cost peradditional unit of output
![Page 30: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/30.jpg)
Profit Max Input Side = Profit Max Output Side
![Page 31: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/31.jpg)
Profit Max-Output Side(Alternative Cases)
Case TR TC
1 Linear Linear
2 Linear Nonlinear
3 Nonlinear Linear
4 Nonlinear Nonlinear
![Page 32: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/32.jpg)
Profit Max Level of Output
Nonlinear TR & Nonlinear TC Decreasing MR, Increasing MC
![Page 33: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/33.jpg)
The ‘Profit’ Equation
= TR – TC= TR – TVC - TFC= PQ – (AVC)Q – TFC= (P-AVC)Q – TFC= (P-AVC)Q – (AFC)Q= (P-AVC-AFC)Q= (P-ATC)Q
![Page 34: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/34.jpg)
P Setter π
![Page 35: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/35.jpg)
P Taker π
![Page 36: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/36.jpg)
Four Math Cases/Examples of Profit Maximization
Case TR MR TFC TVC TC MC
1 10q 10 120 4q 120+4q 4
2 10q 10 120 .1q2 120+.1q2
.2q
3 44q-q2 44-2q 120 4q 120+4q 4
4 44q-q2 44-2q 120 .1q2 120+.1q2
.2q
![Page 37: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/37.jpg)
Breakeven (B.E.) Analysis
= 0 TR – TVC – TFC = 0 PQ – (AVC)Q – TFC = 0
equation w/4 variables(P, Q, AVC, TFC)
given any 3, solve for 4th
B.E. Q = TFC/(P-AVC) B.E. P = AVC + AFC
Note: analysis = desired amt
![Page 38: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/38.jpg)
Case #1 – Breakeven Q
TR = TC 10q = 120 + 4q 6q = 120 q = 20Check: TR = 10q =
10(20)= 200
- TFC -120 -120 -120
- TVC -4q -4 (20) -80
= = = = 0
![Page 39: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/39.jpg)
B.E. Q due to P to $8 (From $0)
TR = TC 8q = 120 + 4q 4q = 120 q = 30
![Page 40: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/40.jpg)
Case #1 Max
MR = 10 > MC = 4 Keep increasing q to increase profit
![Page 41: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/41.jpg)
TR for a P Setting Firm (sets P but Q sold is variable) e.g. P2
< P1
$
Q
TR1 (P = P1)
TR2 (P = P2)
![Page 42: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/42.jpg)
Case #2 - Max
MR = MC 10 = .2q q* = 50 Max = TR = 10q = 10(50) = 500
- TFC -120 -120 -120
- TVC -.1q2 -.1(50)2 -250
= 130
![Page 43: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/43.jpg)
Quadratic Formula
= formula that finds values of X that result in a quadratic equation’s value = 0
Equation: aX2 + bX + c = 0
Formula: X = b and b ac
a
( )2 4
2
![Page 44: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/44.jpg)
Case #2 Breakeven Q
TR = TC 10q = 120 + .1q2
.1q2 – 10q + 120 = 0
a=.1, b=-10, c=120
q
and
( ) ( ) (. )( )
(. )
.
.
.
.
. .
1 0 1 0 4 1 1 2 0
2 1
1 0 1 0 0 4 8
2
1 0 5 2
2
1 0 7 2 11
2
8 6 0 6 1 3 9 5
2
Check:q=86.06TR-TC=10(86.06)-
120-.1(86.06)2
= 860.6-120-740.6=0
Q=13.95TR-TC=10(13.95)-120-.1(13.95)2
= 139.50-120-19.50=0
![Page 45: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/45.jpg)
Stay-even Analysis
=> Determining the volume required to offset a change in costs, prices, or other factors.
=> Set profit equations equal and solve for unknown.
=> Π1 = Π2
=> P1Q1 – AVC1Q1 – TFC = P2Q2 – AVC2 Q2 - TFC
![Page 46: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/46.jpg)
For which of the following situations would the farmer produce corn in the SR?
A. Price of corn = $2.00, AVC = $1, TFC = $100
B. Price of corn = $1.75, TVC = $1.50Q, TFC = $100
C. Price of corn = $2.50, TVC = $2.75Q, TFC = $100
D. Price of corn = $2.00, AVC = $1.00, TFC = $400
E. Price of corn = $1.75, TVC = $1.50Q, TFC = $275
![Page 47: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/47.jpg)
Produce or Shut Down in SR?
Let p = max by producing
= TR – TVC – TFC SD = Max if shut down
= - TFC Produce if p > SD
TR - TVC – TFC > -TFC TR – TVC > 0 TR > TVC TR/q > TVC/q P > AVC
![Page 48: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/48.jpg)
Shut Down Profits
![Page 49: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/49.jpg)
Output q produced by a P-taking firm
![Page 50: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/50.jpg)
Shut Down Graph
![Page 51: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/51.jpg)
Derivation of Market S (Qs) from Firm S (qf)
P = MC P = 5 + 10qf
10q* = -5 + P
qf = -1/2 + .1P
qs = 100qf = -50 + 10P
10P = 50 + Qs
P = 5 + .1Qs
![Page 52: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/52.jpg)
LR Output P Disequilibrium
![Page 53: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/53.jpg)
LR Output P Equilibrium
![Page 54: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/54.jpg)
LR Break Even ?
While firms may stay in business in the SR even though they are losing money, in the LR firms need to make money.
In LR, firms need to cover all costs and have a NPV > 0.
![Page 55: Unit 6. Analyses of SR Costs & Profits as Functions of Output Q](https://reader036.vdocuments.mx/reader036/viewer/2022081519/56649f055503460f94c1971a/html5/thumbnails/55.jpg)
Real-World Cost Analysis Complexities
1. Need to calculate costs of multiple variable and multiple fixed inputs.
2. Some individual inputs may have fixed and variable components.
3. Some inputs are use to produce multiple outputs, so need to allocate or assign input costs across products.
4. Calculating input costs often more difficult than a simple input price x input quantity calculation (e.g. how to value/cost depreciable inputs).