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The Firm and Profit Maximization
Overheads
Neoclassical firm -
A neoclassical firm is an organization that controls the
transformation of inputs (resources it owns or purchases)
into outputs (valued products that it sells),
and earns the difference between what it receives
in revenue, and what it spends on inputs
We define the production function as
f represents the relationship between outputs and inputs
xj is the quantity used of the jth input
(x1, x2, x3, . . . xn) is the input bundle
n is the number of inputs used by the firm
y represents output
f(x) maxy
[y: (x, y) is an element of the production set]
f(x1 , x2 , x3 , ) maxy ε P(x)
[y]
Returns (Profit)
The profit from a production plan is the revenue obtained
from the plan minus the cost of inputs used to implement it
π p y w1x1 w2x2
π p y Σn
i 1wixi
π Revenue Costs
Objectives of the firm
We typically assume that a firm existsin order to make money
A firm that wants to make money is called a for-profit firm, or a profit maximizing firm
The firm maximizes the returns from thetechnologies it controls taking into account:
Given the profit max assumption
The demand for final consumption goods
Opportunities for buying and selling factors / products
The actions of other firms in the market
The profit max problem
π(p , w1, w2 , ) maxx, y
p y Σn
i 1wixi such that y ε P (x)
π(p , w1 , w2 , ) maxy
py C(y , w1 , w2 , )
π(p, w1, w2 , ) maxx
pf (x1 , x2 , , xn) Σn
i 1wixi
What is profit?
Profit is revenue minus costs or
π Revenue Costs
R C
Explicit and implicit costs
Explicit costs
1. purchase of expendable inputs including labor time
2. purchase of capital services (usually rent or lease)
Implicit costs
1. value of produced expendables(feed for a cattle producer)
2. value of services provided by owned capitalincluding financial capital and charges such as implicitrent, depreciation, compensation for operator labor, etc.
Accounting profit
Accounting cost
Accounting profit
+ depreciation on plant & equipmentexplicit costs
total revenue - accounting cost
Economic profit
Economic cost
Economic profit
+ all implicit costsexplicit costs
total revenue - economic cost
Why do we use economic profit?
To reflect total costs and revenues for a decision
To account for all resources used in production
Why do profits exist?
All factors of production receive a payment
Expendables receive their market price
Labor receives wages
Land receives rent
Capital receives interest
Firm owners receive profits
What are profits?
Profits are the returns to
Innovation
Risk
production
delivery
new products
The Profit Maximizing Output Level
Profit = Revenue - Cost = R - C
π Revenue Cost
pf (x1 , x2 , , xn) Σn
i 1wixi
py C(y , w1 , w2 , ,wn)
Demand
The individual demand curve facing a firm tells us, for different prices, the quantity of output that customers will choose to purchase from the firm
The demand curve facing the firm show us themaximum price the firm can charge to sellany given amount of output
Example Inverse Demands
p = 320 - 20y
p = $1.85
Total Revenue
Revenue is the total income that comes from thesale of the output (goods and services) of a givenfirm or production process
Revenue R(p , y) py pf (x1 , x2 , , xn )
Y Price FC VC C TR Profit0.00 320 120 0.00 120.00 0 -120.00
1.00 300 120 64.00 184.00 300 116.00 2.00 280 120 130.00 250.00 560 310.00 3.00 260 120 204.00 324.00 780 456.00
4.00 240 120 292.00 412.00 960 548.00
5.00 220 120 400.00 520.00 1100 580.00
Y Price FC VC C TR Profit0.00 320 120 0.00 120.00 0 -120.00 1.00 300 120 64.00 184.00 300 116.00 2.00 280 120 130.00 250.00 560 310.00 3.00 260 120 204.00 324.00 780 456.00 4.00 240 120 292.00 412.00 960 548.00 5.00 220 120 400.00 520.00 1100 580.00 6.00 200 120 534.00 654.00 1200 546.00 7.00 180 120 700.00 820.00 1260 440.00 8.00 160 120 904.00 1024.00 1280 256.00 9.00 140 120 1152.00 1272.00 1260 -12.00 10.00 120 120 1450.00 1570.00 1200 -370.00 11.00 100 120 1804.00 1924.00 1100 -824.00 12.00 80 120 2220.00 2340.00 960 -1380.00 14.00 40 120 3262.00 3382.00 560 -2822.00 16.00 0 120 4624.00 4744.00 0 -4744.00
Total cost
Cost TC C(x1 , x2 , , w1 , w2 , )
Σn
i 1wixi
C(y , w1 , w2 , )
Maximizing profit
Choose the level of output wherethe difference between TR and TCis the greatest
Y Price FC VC C TR Profit0.00 320 120 0.00 120.00 0 -120.00
1.00 300 120 64.00 184.00 300 116.00 2.00 280 120 130.00 250.00 560 310.00 3.00 260 120 204.00 324.00 780 456.00
4.00 240 120 292.00 412.00 960 548.00
5.00 220 120 400.00 520.00 1100 580.00 6.00 200 120 534.00 654.00 1200 546.00 7.00 180 120 700.00 820.00 1260 440.00 8.00 160 120 904.00 1024.00 1280 256.00 9.00 140 120 1152.00 1272.00 1260 -12.00 10.00 120 120 1450.00 1570.00 1200 -370.00 11.00 100 120 1804.00 1924.00 1100 -824.00 12.00 80 120 2220.00 2340.00 960 -1380.00
Y Price FC VC C TR Profit0.00 320 120 0.00 120.00 0 -120.00 1.00 300 120 64.00 184.00 300 116.00 2.00 280 120 130.00 250.00 560 310.00 3.00 260 120 204.00 324.00 780 456.00 4.00 240 120 292.00 412.00 960 548.00
5.00 220 120 400.00 520.00 1100 580.00
6.00 200 120 534.00 654.00 1200 546.00 7.00 180 120 700.00 820.00 1260 440.00 8.00 160 120 904.00 1024.00 1280 256.00 9.00 140 120 1152.00 1272.00 1260 -12.00 10.00 120 120 1450.00 1570.00 1200 -370.00 11.00 100 120 1804.00 1924.00 1100 -824.00 12.00 80 120 2220.00 2340.00 960 -1380.00 14.00 40 120 3262.00 3382.00 560 -2822.00 16.00 0 120 4624.00 4744.00 0 -4744.00
Marginal cost (MC)
Marginal cost is the increment, or addition,to cost that results from producingone more unit of output
MC ΔC(y,w)Δy
ΔTC(y,w)Δy
y Price FC VC C AFC AVC ATC MC TR MR Profit0.00 320 120 0.00 120.00 0 -120.00
64.00 300.00 1.00 300 120 64.00 184.00 120.00 64.00 184.00 300 116.00
66.00 260.00 2.00 280 120 130.00 250.00 60.00 65.00 125.00 560 310.00
74.00 220.00
3.00 260 120 204.00 324.00 40.00 68.00 108.00 780 456.00
88.00 180.00
4.00 240 120 292.00 412.00 30.00 73.00 103.00 960 548.00108.00 140.00
5.00 220 120 400.00 520.00 24.00 80.00 104.00 1100 580.00134.00 100.00
6.00 200 120 534.00 654.00 20.00 89.00 109.00 1200 546.00166.00 60.00
7.00 180 120 700.00 820.00 17.14 100.00 117.14 1260 440.00204.00 20.00
8.00 160 120 904.00 1024.00 15.00 113.00 128.00 1280 256.00248.00 -20.00
9.00 140 120 1152.00 1272.00 13.33 128.00 141.33 1260 -12.00298.00 -60.00
10.00 120 120 1450.00 1570.00 12.00 145.00 157.00 1200 -370.00
MC ΔC(y,w)Δy
(412 324)(4 3)
881
88
y Price FC VC C AFC AVC ATC MC3 260 120 204.00 324.0 40.00 68.00 108.00
88.004 240 120 292.00 412.0 30.00 73.00 103.00
108.005 220 120 400.00 520.0 24.00 80.00 104.00
Marginal Revenue (MR)
MR ΔR(y,p)Δy
ΔTR(y,p)Δy
Marginal revenue is the increment, or addition,to revenue that results from producingone more unit of output
Marginal revenue is the change in total revenuefrom producing one more unit of output
y Price FC VC C AFC AVC ATC MC TR MR Profit
0 320 120 0.00 120.0 0 -120.064.00 300.0
1 300 120 64.00 184.0 120.00 64.00 184.00 300 116.066.00 260.0
2 280 120 130.00 250.0 60.00 65.00 125.00 560 310.074.00 220.0
3 260 120 204.0 324.0 40.0 68.0 108.0 780 456.0
88.00 180.04 240 120 292.0 412.0 30.0 73.0 103.0 960 548.0
108.00 140.05 220 120 400.00 520.0 24.00 80.00 104.00 1100 580.0
134.00 100.06 200 120 534.00 654.0 20.00 89.00 109.00 1200 546.0
166.00 60.07 180 120 700.00 820.0 17.14 100.00 117.14 1260 440.0
204.00 20.08 160 120 904.00 1024.0 15.00 113.00 128.00 1280 256.0
y Price TR MR Profit3.00 260 780 456.0
180.04.00 240 960 548.0
140.05.00 220 1100 580.0
100.06.00 200 1200 546.0
MR ΔTR(y,p)Δy
(960 780)(4 3)
1801
180
y Price TR MR Profit3.00 260 780 456.0
180.04.00 240 960 548.0
140.05.00 220 1100 580.0
100.06.00 200 1200 546.0
Another example Increase output from 4 to 5 units
MR ΔTR(y,p)Δy
(1100 960)(5 4)
1401
140
A note on marginal revenue and price
Marginal revenue is always less than price
The firm must lower price in order to sell more units
WHY?
p
qq0
1 2 3 4
p0
5
Revenue Marginal Revenue
Marginal Revenue = p0
The lower price applies to all units and so the revenue per unit will be less than the price
p0
q0
p1
q1
B
A
p
q
Demand
MR = A - B
Profit Max Using MR and MC
An increase in output will always increase profit
if MR > MC
An increase in output will always decrease profit
if MR < MC
The rule is then
Increase output whenever MR > MC
Decrease output if MR < MC
y Price C MC TR MR Profit3.00 260 324.00 780 456.00
88.00 180.00 4.00 240 412.00 960 548.00
108.00 140.00 5.00 220 520.00 1100 580.00
134.00 100.00 6.00 200 654.00 1200 546.00
Example
Should we increase output from 3 to 4?
Should we increase output from 4 to 5?
Should we increase output from 5 to 6?
Yes
Yes
No !
Profit Maximization Using Graphs
Profit is positive if TR > TC
0200400600800100012001400160018002000
0 2 4 6 8 10 12 14 16 18Output
$
TRC
Profit Maximization Using MR and MC
Profit on a given unit is positive if MR > MC
050100150200250300350400
0 2 4 6 8 10 12 14 16 18Output
$ MC
DemandMR
Two intersections of MC and MR
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14 16 18 20Output
$
MC
DemandMR
The optimal output level occurs where MC intersects MR from below
0
50
100
150
200
250
300
0 2 4 6 8 10 12 14 16 18 20Output
$
MC
DemandMR
Why average costs are irrelevant in the short-run
The short-run decision is whether to produceone more unit or not
Only marginal cost and marginal revenueare relevant for this decision
Marginal Decision Making and Short-run Decisions
The marginal approach to profit statesthat a firm should take any action that addsmore to its revenue than to its cost
Examples where marginal decision making is relevant
advertising
cost efficiency consultant
adding a salesperson
sprucing up sales area
adding a two-year warranty to product
The shutdown ruleDo we keep producing if we are losing money?
It depends on what we mean by a loss
It depends on whetherwe are in the short-run or in the long run
It depends on which costs are fixed,which are variable, and which are sunk
Case 1 - TC > TR at all Q
TR > TVC where MR = MC
TC > TR at all Q
TR > TVC whereMR = MC
0255075100125150175200
0 1 2 3 4 5 6 7 8 9 10Output - y
Co
st
VC
CTR
Marginal Cost & Revenue Curves
0510152025303540
0 1 2 3 4 5 6 7 8 9 10Output - y
Co
st MC
MR
Total Cost & Revenue Curves
In the short-run fixed costs must be paidindependent of the level of output
At 6 units of output, total revenue more thancovers total variable costs,
leaving a residual to help cover fixed costs
So the firm should produce 6 units in the short run
The shutdown rule
In the short-run, the firm should continue to produceif total revenue exceeds total variable costs;
otherwise, it should shut down
Case 2 - TC > TR at all Q
TR < TVC where MR = MC
TR < TCat all Q
TR < TVC whereMR = MC
Total Revenue and Cost Curves
0102030405060708090
0 1 2 3 4 5 6 7Output - y
Co
st
TVC
CTR
Marginal Revenue and Cost Curves
048121620242832
0 1 2 3 4 5 6 7Output - y
Co
st MC
MR
The shutdown rule
In the short-run, the firm should continue to produceif total revenue exceeds total variable costs;
otherwise, it should shut down
Shutdown in the long-run
In the long-run the firm should exitthe industry if it has any size loss
Shutdown and fixed costs that are not sunk
In the short-run, if some of the fixed costs are not sunk,the firm may be better off to not operate when TR > TVC,if it can recover most of its sunk costs that are fixed costs,by shutting down
Suppose at 6 units of output, TFC =$50, TVC = $60 and TC = $110
But suppose that only $10 of the fixed costs are sunk,so that by shutting down the firm can recover $40.00 of fixed cost
Suppose at 6 units of output, that total revenue is equal to $95.
By operating the firm can make $35 over variable costs
The firms net loss is then just $15.00
The firm's net loss by shutting down is only $10.00
The firm is better off by shutting down
This will help cover the the fixed costs of $50
(95 - 60)
(35 - 50 or 95 - 110)
Asset Fixed Variable Total Sales Disposal Total Profit/
Cost Cost Cost Revenue Revenue Revenue LossOperate 50 60 110 95 0 95 -15Shut-down 50 0 50 0 40 40 -10
The End