Transcript Week 2 Section Notes - Open Computing Facility

Section 4 Section Notes
EWMBA201A
Eva Vivalt
September 19, 2009
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Administrative Stuff
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Recap of evaluations:
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4.
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More of everything: intuition (helping with thought problems),
numbers problems, extra problems, real-world examples.
Questions that are less crucial can be saved for after class.
Extra time after class.
I’ll distribute a pre-exam guide with more sample problems to work
through and if you have questions on them you can ask me in office
hours after section.
Sunk costs and Mid-term
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Recap of Costs
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Sunk Costs
“Don’t worry about things you cannot change”
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Opportunity Costs
“Always know what ALL your options are”
Over the relevant time horizon…
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Total Costs: C(q)
Fixed Costs: Not dependant on quantity produced: C(0)
Variable Costs: C(q)-C(0)
Marginal Costs: Cost of increasing q by a small amount: dC(q)/dq
Average Total Costs: C(q)/q
Average Variable Costs: vC(q)/q
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All the calculus it might be helpful to
know
• Derivative of A + BQ + CQ2 = B + 2CQ
• To minimize or maximize something:
– 1) Take its derivative (with respect to whatever it is
that we are choosing, e.g. quantity to produce).
– 2) Set it equal to 0.
– 3) Solve for what we are choosing (e.g. Q).
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Thought Exercise
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What’s the difference between average cost and marginal cost?
Between average variable cost and marginal cost?
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Thought Exercise
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What’s the difference between average cost and marginal cost?
Between average variable cost and marginal cost?
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Marginal cost is the incremental cost of producing an additional
unit. Average cost is the per unit cost of production, over all units
produced.
Side: average total cost divides both variable and fixed costs over
the total production. Average variable cost averages only variable
costs over the output.
Marginal cost looks only at the cost of producing an extra unit.
Average variable cost is the average variable cost across all output
at a certain level.
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What do these functions look like?
Cost ($)
Total Cost
Variable Cost
Fixed Cost
Q
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What do these functions look like?
Cost ($)
MC
ATC
AVC
Q
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Why do we care what these look like?
• Knowing what things look like, what they
include, and understanding how the curves
relate to each other is helpful for building
intuition, which is key to answering thought
questions (or any questions). E.g. tax question
on midterm – if you read the question
carefully, and you understand the demand and
supply curves, you should be able to modify
their equations properly.
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Question 2 on problem set
• A) To minimize total costs, with
C(Q)=405+20Q+5Q2 we set Q=?
• Then profits = 120*(0)-(405+20*(0)+5(0)2)
= -405
• B) To maximize sales, assuming that
everything produced will be bought, produce
the maximum possible: Q = 100.
• Then profits = 120*100-(405+20*100+5*1002)
= -40,405
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• C) To minimize ATC, differentiate with respect
to quantity (the thing that we are picking) and
set that equal to 0:
• (Notation: ATC=AC, TC=C)
• ATC=TC/Q=405/Q+20+5Q = 405*Q-1+20+5Q
• Differentiating: -405*Q-2+5
• Setting it equal to 0: -405*Q-2+5=0
• Solving: -405*Q-2=-5  405/5=Q2  Q=9
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• Alternative way for C:
• We know ATC=MC at the minimum of ATC.
• We also know ATC=TC/Q=405/Q+20+5Q =
405*Q-1+20+5Q.
• We also know MC=derivative of TC with
respect to Q=20+10Q.
•  405*Q-1+20+5Q=20+10Q  405*Q-1=5Q
 405=5Q2  Q=9
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• D) To maximize profits under perfect
competition, set MC=price.
• MC = 20 + 10Q
• P = 120
•  20 + 10Q = 120  Q = 10
• Thought question: why is this higher than the
Q we found in part C?
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• What does MC actually look like for this
question?
• You check this later (analogous problem later
this section): Does this industry have
economies of scale or diseconomies of scale?
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Question 3 on problem set
• A) TR = P(Q)*Q = 100Q-Q2
• MR = dTR/dQ = 100-2Q
• When you’re a monopoly, max profits by
setting MC=MR.
• Remember MC=dTC/dQ=10.
• 10=100-2Q  Q=45
• Profit = TR – TC = P(Q)*Q – (100 + 10Q) =
55*45 – (100+10*45) = 1925
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• B) We still want MC = MR.
• Can we get MC = MR for any of the three ranges?
• If Q is equal to 20, MC =10, MR = 100-2*20=60. If
Q is less than 20, MR is even bigger.
• If Q is equal to 50, MC = 8, MR = 100-2*50=0. So
MC and MR must cross somewhere between 20 and
50.
• Setting MC = MR  100-2Q=8  Q=46, P=54,
Profits=54*46-(100+10*20+8*26)=1976
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• C) We want MC = MR since we’re a
monopoly.
• TC = 100 + Q2  MC = 2Q
• TR = P(Q)*Q = (20-Q)*Q  MR = 20 - 2Q
• MC = MR  2Q=20-2Q  4Q=20  Q=5
• P=15, Profits = TR – TC = 15*5 – 125 = -50
•  Shut down. You’ve done all you possibly
can to maximize profits (MC = MR) and you
still lose money.
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• Real world:
A lot of firms don’t decide how to pick Q based
on carefully comparing MC to P or MC to MR.
Why? Why should we not worry?
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Extra Problem
Given a cost function: C(Q)=10+2Q+0.5Q2
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What are the fixed costs? What are ATC, AVC, MC?
At what Q is ATC is minimized?
Does this function exhibit economies of scale?
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Extra Problem
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Given a cost function: C(Q)=10+2Q+0.5Q2
What are the fixed costs? What are ATC, AVC, MC?
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Fixed costs are 10.
ATC=C(Q)/Q=10/Q+2+0.5Q
AVC=VC/Q=2+0.5Q
MC=dC(Q)/dQ= 2+Q
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Extra Problem
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Given a cost function: C(Q)=10+2Q+0.5Q2
At what Q is ATC is minimized?
From last slide: ATC=C(Q)/Q=10/Q+2+0.5Q
To find where ATC is minimized, set dATC/dQ = 0
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dATC/dQ= -10/Q2 +0.5=0
 Q=2√5
Alternately, recall that ATC is minimized where ATC=MC.
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10/Q+2+0.5Q=2+Q
Q=2√5
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Extra Problem
Given a cost function: C(Q)=10+2Q+0.5Q2
Does this function exhibit economies of scale?
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Recall from lecture that economies of scale describe how the firm’s
average costs change as output increases.
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If ATC increase with quantity, we have “diseconomies of scale”.
If ATC decrease with quantity, we have “economies of scale”.
Let’s check for our case:
ATC=C(Q)/Q=10/Q+2+0.5Q
dATC/dQ= -10/Q2 +0.5  If we set this equal to 0, we find 20=Q2  at
Q=√20 we have a min.
 For some values of Q we have “economies of scale” and for other values
we have “diseconomies of scale”.
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Common Midterm Mistakes
The final will be cumulative, so the material
from the first part is still relevant.
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• 5) Please be precise and accurate. E.g. avoid “weasel words”
like “may”, “might”, “could”, “likely”, “probably”, “possibly”, “potentially”…
unless you really do mean that it is uncertain. E.g. if something
is perfectly inelastic, it’s not just relatively inelastic – it
doesn’t respond to price at all.
• 4) Not listing all the possible actions a risk-loving/risk-averse
Martha might take.
• 3) Maximizing profits is not the same as maximizing revenue.
We care about profits when making decisions (see question 3b
in this problem set).
• 2) Price elasticity of durables vs. non-durables (similar to #5:
be comprehensive).
And, the #1 mistake…
• 1) Not reading the question.
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