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Chapter 13 Technology, Production, and Costs
A. General Terms
1. Business Firm – an organization owned and operated by private individuals that
specialize in production
2. Production – the process of combining inputs to make output
Illustration: input 
Process production
 output
3. Decision Maker- person in the firm that decides on day to day actions of firm. If we
are considering corporations this would be management.
4. Customer – purchasers of goods and services. It should be noted that they are HH,
gov’t, and firms.
5. Profit – Total Revenue – Total Costs = Profit
**We assume that firms are profit maximizers. They are not revenue or sales
maximizers.
6. Stakeholder vs. Shareholder Model
a. Stakeholder Model – in this model firms seek to maximize the benefit of all those that
have an interest in the firm and not just the share price of the owners. Some goals are:
-employment for people in the area
-taxes for government
-low pollution
-sustainable business
-maximize profit for owners
b. Shareholder Model – this is what we typically assume. Those firms are in business to
make profits for the owners. Although other interests might be considered it is all in
attempt to earn higher profits.
7. Problems in Firms that Inhibit Profit Max
a. Communication difficulty as the size becomes larger. So deciding on the optimal size
is very important.
b. Monitoring workers; this is the principal-agent problem that was discussed earlier.
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B. Production
1. Technology – the means by which you combine inputs to produce output. We are not
concerned with innovation unless is serves to increase productivity.
-it is assumed fixed at a given point in time.
2. Short-Run vs. Long-Run
a. Short-Run (SR) – a time horizon that has at least one variable fixed. For our purposes
we assume that it is K. Generally only labor can change in the SR.
b. Long-Run (LR) – When all variables are allowed to change. The time is arbitrary and
depends on the industry or market.
3. Type of Inputs
a. Fixed Input – input whose quantity does not vary as output goes up. In the SR we
assume that K is fixed.
b. Variable Input – input whose quantity changes as output goes up.
4. Production Function – This is a function that gives us the maximum output that can
be produced for different combinations of inputs. It is over some specified period of
time.
In general: Q = f (K, L)  if we look in the SR we look at Q = f (L)
5. Total Product Curve – (TPC) – this shows the maximum output graphically that can
be obtained from a given combination of inputs.
Graphically:
Output
(Q)
Total Product
(TP)
Labor (L)
L*
Properties:
(a) The curve increases at an increasing rate and then at a decreasing rate. This gives us
MP and returns to scale
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(b) The curve begins to slope back on itself beyond L*. So adding more labor beyond
this only serves to drop productivity. We can say we max out productivity at L*.
6. Marginal Productivity of Labor and Average Product of Labor(MPL APL) –
MPL -The additional output that results from increasing one more unit of labor. Note that
one unit might not necessarily be one person.
-we get this due to the fact that capital is fixed. After we move beyond the optimal K/L
ratio marginal productivity starts to drop.
APL – this is the average output per person. This is what a person produces on average.
a. Mathematically: MPL = ∆ Q / ∆ L & APL = Q / L
b. Finding with the Total Product Curve:
Step 1: Draw and Label TP curve
Step 2: Label 1-unit increments on the horizontal axis
Step 3: Draw up to the curve and over to the Q-axis
Step 4: Label MP’s on the vertical axis
Graph 1: Getting MP
Output
(Q)
MP4
Total Product
(TP)
MP3
MP2
MP1
Labor (L)
L*
Graph 2: Graph of MP’s and AP
Output
(Q)
Marginal
Product (MP)
Average Product
(AP)
Labor (L)
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7. Increasing and Decreasing Marginal Returns to Labor
a. Increasing Marginal Returns to Labor – this is when the curve is increasing and an
increasing rate (i.e. steep slope) and we get increasing MP’s. This can be seen above
from MP1-MP3.
b. Decreasing Marginal Returns to Labor – this is when the curve is increasing at a
decreasing rate and we get MP’s dropping. This can be seen from MP3-MP4.
C. Costs
-Main objective of a firm is to maximize profits. This is the same thing as minimizing
costs. Also, note that OC’s are included in costs for an economist.
1. Sunk Costs – cost that was paid in the past and cannot be recovered. It should not
enter into present decisions. It might be more appropriate to model a cost as partially
sunk rather than completely sunk.
2. Explicit vs. Implicit Cost
a. Explicit – money paid for an input. This would be something like wages or rent.
These costs include both direct and indirect accounting costs.
b. Implicit – cost for an input that there is not a direct money payment. This is the OC
for owners using resources.
3. Fixed vs. Variable Costs
a. Fixed- cost of a fixed input. This is capital in the SR; rent of capital = r
b. Variable – cost of an input that is allowed to vary with Q. This is labor in the SR;
wages = w
4. Short Run (SR) vs. Long Run (LR)
a. SR – this is the timeframe that is required to make at least one input fixed. We
generally fix capital, due to its relative inability to change quickly. The time is
completely arbitrary and depends on the market or industry.
b. LR – this is the time that is required to make all inputs variable (both K, L).
5. Total Cost (SR) - this is the total cost associated with production. It included both
fixed and variable components.
a. mathematically: TC = TFC + TVC
TFC - total cost of fixed inputs
TVC - total cost of variable inputs
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Total Cost
(TC)
Cost (C)
b. graphically:
Total Variable
Cost (TVC)
Total Fixed
Cost (TFC)
Output (Q)
Note: the fixed cost is the distance between the TVC and TC. We know this due to the
expression of TC - TVC = TFC
6. Average Costs (SR): To obtain average costs we simply divide by Q for all the total
cost components.
Mathematically: 1/Q * [TC = TFC + TVC]  TC/Q = TFC/Q + TVC/Q  ATC=AFC
+ AVC
Note: we still have that total cost is a function of both the fixed and variable components.
a. AFC - the fixed cost component of each unit of production. As Q ↑ we find that AFC
↓. This is due to the fact that Q increases TFC remains constant.
b. AVC – the variable costs component of each unit production. We can also derive the
shape form the TVC curve. We see that TVC flattens out, so AVC must be getting
smaller and eventually reach a low point. As Q ↑ we see that TVC rises quickly, so AVC
must rise. This gives us a typical U-shape.
c. ATC – the total cost per unit of production. It is u-shaped and mimics the shape of the
AVC curve. Note: that ATC and AVC get closer together as Q ↑ due to the fact that
ATC=AFC + AVC and AFC is getting smaller (i.e. getting closer to 0) as Q ↑.
Graphically:
MC
Cost/Unit
ATC
AVC
AFC
Q
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7. Marginal Cost (MC) – this is the additional cost associated with one more unit of
production. It might not be the case that 1-unit = 1 (i.e. 1-unit could be 25 pieces of
output).
a. mathematically: MC = ∆ Total Cost / ∆ Q = ∆ Total Variable Cost / ∆ Q
b. note that MC intersects AVC and ATC at their lowest point. This all stems from the
fact that:
marginal > avg  avg ↑
marginal < avg  avg ↓
marginal = avg  same
c. The curve looks the way it does based on the productivity of labor. If we look at the
APL we can see that as it tops out we get MC hitting its lowest point.
Q
MC
Cost
APL
L
Q
L*
Q*
If we look at the curves above we note that as average product is at its max we get
marginal costs as their lowest points. This is due to the expressions below.
8. LR Costs
-Recall that in the LR we have that all inputs are allowed to vary. So due to this fact we
make certain assumptions about our LR cots.
a. Least Cost Rule – at any level of Q, a firm chooses the mix of K, L that minimizes cost
for that level of Q. We assume that there is some positive level of production or Q > 0.
b. LR Total Cost (LRTC) – the cost of producing at each level of output. Recall that in
the LR we have no FC, so if Q = 0, then there is no cost.
c. Long Run Average Cost- (LRAC) – this is the LR cost per unit. It is the minimum of
all SRATC curves due to the fact that in the LR each firm will choose the least cost
amount of K, L to produce at each unit. So given this choice once you choose output,
you choose the K, L that minimizes this cost due to the profit maximizing assumption.
Mathematically: LRAC = LRTC / Q
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d. Long Run Marginal Cost – (LRMC) – this is the marginal cost per unit. It is LRTC
mathematically: MC = ∆ LR Total Cost / ∆ Q
note: It is derived in the same way as all MC’s and has the same relationship to LRAC as
we defined earlier for the SR curve.
Comparing SR vs. LR
LR cost curves are different from the SR because we have both K and L able to vary in
the LR, while in the SR we must include fixed costs. When a decision-maker chooses in
the LR all possible combinations of K, L and scales of production are possible for the
goal of profit maximization.
Note: A LRTC curve starts at (0, 0) while a SRTC curve does not. This is due to no
sunk costs in the LR.
Cost/Unit
LRMC LRAC
LRTC
Q
Q
The LTC illustrates total cost in the LR. Costs go up and then begin to increase less
rapidly and then increase in rate past a certain point. This is directly due to the U-shape
of the LRAC. After LRAC begins to increase the LTC begins to increase faster. This is
due to the fact that the cost per unit is going up. The LRAC has its shape because of the
LRMC. We get an increase in MC because productivity begins to drop as we use inputs
more intensively. The LRMC intersect the LRAC at its lowest point. If LRMC<LRAC
then LRAC is decreasing and when it is greater LRAC is increasing.
Note: (1) Show how to derive the LRAC &
(2) Show how to go from LR to SR back to LR.
9. Returns to Scale – refers to how costs are affected as we increase or decrease output
level.
a. Economies of Scale - Economies of scale refer the decreasing costs on a LRAC curve.
The costs decrease for two reasons:
(i) as scale increases the costs decrease due to use of larger or more efficient capital
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(ii) as there is an increase in production there are decrease in costs due to specialization
and learning.
b. Diseconomies of Scale - refer the increasing costs on a LRAC curve.
The costs increase for two reasons:
(i) as scale increases the costs increase due to the fact that communication and cohesion
between departments and units becomes more difficult.
(ii) as there is an increase in production it becomes more difficult to oversee workers.
There is little oversight or the principal-agent problem.
Note: Constant returns to scale can also occur. This is when we have costs constant as Q
increases
LRAC
Cost/Unit
Economies of
scale
Diseconomies
of scale
Q
D. Profit Maximization in General
-assume that firms are profit maximizers. This is the goal of all firms which is akin to
cost minimization.
1. Types of Profit
a. accounting profit – this does not include OC.
b. economic profit – this is TR-TC (explicit and implicit costs)
-explicit costs – where money is paid for the use of resources
-implicit costs – the OC that is incurred for using your resources of production
Note: to determine how firms operate and make decision we assume that they look at
economic profit and not accounting profit.
** we can look at economic profit as the above normal rates of return that are gained by
going into business.
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2. Reasons for Profit
a. risk-taking – people are rewarded for the risks that they bear while going into business.
b. innovation – people are rewarded for new ideas and thoughts. This means that
property rights somehow have to be enforced.
Ex. New technology or method of production, new location, etc…
3. Firms Constraints and How they Factor into Profit
-these are the things that limit a firm in production
a. Demand or Quantity Constraint – this is the Qd that will be demanded by consumers
from a firm. We should note that once a Q is chosen the price that firms can charge is
automatically determined by finding the corresponding P on the demand curve.
-
a firm can choose either P or Q, but not both.
b. Total Revenue – This is the total amount received by selling output. It would be
summing up all the prices of G/S sold or if price is the same:
TR = P * Q
c. Cost Constraint – This is the budget that a firm has. We assume that a firm is only
spending on K, L for simplicity.
TC = r*K + w*L
-after a firm determines Q it determines the optimal amount of K, L to produce that Q at
the least cost.
-both of these constraints give us profit
4. Profit Maximization: Two Methods
a. Total Approach – this uses both TC and TR to find the optimal Q that gives the most
profit for a firm. We simply find where TR and TC are the farthest distance apart.
Graphically:
TC
C, R or $
TR (Market)
Q
Q*
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Profit Max = Q*
We can see it is the
farthest distance
between TR and TC. It
is also the case at Q*
that the tangent lines
are parallel at Q*.
b. Marginal Approach – Here we use marginal cost and marginal revenue to find profit
max. This comes directly out of the fact that the tangent lines are parallel at profit max
output in the total approach.
i. Marginal Cost – The change in total cost by selling one more unit.
ii. Marginal Revenue – The change in TR that occurs when we sell one more unit.
Mathematically: MR = ∆ TR / ∆Q
-we note that MR is dropping since by the law of demand we must drop price to sell more
Q.
iii. MR vs. MC
MR > MC  the increase Q since you are earning profit
MR < MC  decrease Q since you are losing money on these units sold
MR = MC  Stop! Any Q beyond this point will result in less profit and any point
before this will imply you could earn more by selling more.
Graphically:
C, R or $
MC
Profit
Q
Q*
MR
-this is going to be the method that we employ most often in future lectures
Note: if the MC hits the MR curve twice then use the second point. Also, the Q* from
both approaches gives you the same results. The methods just differ in how they arrive at
the same conclusion.
5. Motivation for Firms to Profit Maximize
-if they didn’t they would have to face these actions
a. Other firms entering the market and selling a similar or same product at a lower price.
b. Other firms could take over the existing firm and use their set-up to operate more
efficiently and earn greater profits.
c. S/h could rebel and demand that MGT is changed by going through the BOD. This
would ensure that the people that run the company are striving for profit max.
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6. Shutdown Rule
a. SR- If a firm is not covering costs (i.e. P < ATC) then it must decide whether to
continue production or not. This is the shutdown decision.
Rule:
(1) If we have P > AVC then keep producing. This is due to the fact that they are
covering costs of production of the units and on top of that they are recouping some of
the fixed/sunk costs that were incurred to start production. This is the same as loss
minimization.
(2) If we have P < AVC stop production b/c you are not even covering the costs of
producing the units. This means you are furthering your losses, so you should shutdown.
b. LR – If a firm cannot cover costs in the LR even if it can choose the optimal K, L to
produce a given quantity then either don’t start producing or stop producing.
Note: it could be the case that market changes (i.e. P changes) or that costs change
thereby changing the results above. This might lead to a different conclusion.
7. Principal-Agent Problem – this is when we have agents of the firm that have a
different objective than profit max. They want to keep their job and might try to
maximize something other than profit. To solve for this it is generally the case that you
either:
a. Tie compensation back into profitability. This ensures that s/h goals and MGT goals
are the same.
b. Give the workers a stake in the Co. This gives them the same motivation as s/h and
will motivate them to gear their work towards this goal.
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