September 19, 2009Section 4 Section Notes1 EWMBA201A Eva Vivalt.

September 19, 2009 Section 4 Section Notes 1

Section 4 Section Notes

EWMBA201A

Eva Vivalt

September 19, 2009 Section 4 Section Notes 2

Administrative Stuff

1. Recap of evaluations:1. More of everything: intuition (helping with thought problems),

numbers problems, extra problems, real-world examples.

2. Questions that are less crucial can be saved for after class.

3. Extra time after class.

4. 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.

2. Sunk costs and Mid-term

September 19, 2009 Section 4 Section Notes 3

Recap of Costs• Sunk Costs

“Don’t worry about things you cannot change”

• Opportunity Costs“Always know what ALL your options are”

Over the relevant time horizon…

• 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

September 19, 2009 Section 4 Section Notes 4

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).

September 19, 2009 Section 4 Section Notes 5

Thought Exercise• What’s the difference between average cost and marginal

cost? Between average variable cost and marginal cost?

September 19, 2009 Section 4 Section Notes 6

Thought Exercise• What’s the difference between average cost and marginal

cost? Between average variable cost and marginal cost?

• 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.

September 19, 2009 Section 4 Section Notes 7

What do these functions look like?Cost ($)

Variable Cost

Total Cost

Q

Fixed Cost

September 19, 2009 Section 4 Section Notes 8

What do these functions look like?

Cost ($)

ATC

MC

AVC

Q

September 19, 2009 Section 4 Section Notes 9

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.

September 19, 2009 Section 4 Section Notes 10

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

September 19, 2009 Section 4 Section Notes 11

• 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

September 19, 2009 Section 4 Section Notes 12

• 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

September 19, 2009 Section 4 Section Notes 13

• 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?

September 19, 2009 Section 4 Section Notes 14

• 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?

September 19, 2009 Section 4 Section Notes 15

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

September 19, 2009 Section 4 Section Notes 16

• 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

September 19, 2009 Section 4 Section Notes 17

• 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.

September 19, 2009 Section 4 Section Notes 18

• 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?

September 19, 2009 Section 4 Section Notes 19

Extra Problem

Given a cost function: C(Q)=10+2Q+0.5Q2

• What are the fixed costs? What are ATC, AVC, MC?

• At what Q is ATC is minimized?

• Does this function exhibit economies of scale?

September 19, 2009 Section 4 Section Notes 20

Extra Problem• Given a cost function: C(Q)=10+2Q+0.5Q2

• What are the fixed costs? What are ATC, AVC, MC?

• 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

September 19, 2009 Section 4 Section Notes 21

Extra Problem• 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• dATC/dQ= -10/Q2 +0.5=0 Q=2√5

Alternately, recall that ATC is minimized where ATC=MC. • 10/Q+2+0.5Q=2+Q Q=2√5

September 19, 2009 Section 4 Section Notes 22

Extra Problem• Given a cost function: C(Q)=10+2Q+0.5Q2 • Does this function exhibit economies of scale?

Recall from lecture that economies of scale describe how the firm’s average costs change as output increases.

• 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+0.5QdATC/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”.

September 19, 2009 Section 4 Section Notes 23

Common Midterm Mistakes

The final will be cumulative, so the material from the first part is still relevant.

September 19, 2009 Section 4 Section Notes 24

• 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.