October 3, 2009Final Exam Review1 EWMBA 201A Eva Vivalt

October 3, 2009 Final Exam Review 1

Final Exam Review

EWMBA 201A

Eva Vivalt


Administrative Stuff

1. Final Exam for both sections: Friday October 9th 6pm.

2. Practice questions available on bspace.

3. Pricing project due next Monday or Tuesday.

4. Prof. Vardy’s review before class on Monday and Tuesday.


Today’s Agenda

1. Overview of major course topics (recommend you use this for a review check-list)

2. Tips, focusing mostly on second half since you have previously seen a review on the first half

3. A selection from problem set #5

4. Extra time for questions after section! (Old exams, thought questions, anything….)


The meat of the course

• Basic economic concepts

• Tools for analysis

• Producer’s costs

• Producer’s decision-making/strategies

• Long-run market supply



• Basic economic concepts:– Pareto efficiency as the key criterion – econ

doesn’t care about distribution but efficiency– Perfectly competitive market (conditions for)– Arbitrage– First and second fundamental theorem of welfare– Demand curves, supply curves, movement along

them vs. movement of the curves, and Consumer Surplus



• Tools for analysis (producer or consumer):– Elasticity– Decision trees– Decision-making under risk: Risk neutrality, risk-

loving, risk-aversion• The resulting value of information• An example of what can happen without perfect

information: auctions

– Game theory (Nash equilibria, rationality, common knowledge of rationality)



• Producer’s costs:– Sunk costs

– Opportunity costs

– Total costs, Average total costs

– Fixed costs

– Variable costs, Average variable costs

– Marginal costs

And how these all relate to each other in problems.

- Related: economies of scale/diseconomies of scale



• Producer’s decision-making/strategies– Profit maximization (not revenue maximization)

under perfect competition and monopoly– Price discrimination

• Long-run market supply


Tip!

• Think to yourself: on which of the topics on the previous slides could you be asked a “problem” question? On which of the topics on the previous slides could you be asked a “theory” question? – You know there will be a mix. – You also know that sometimes a problem question

can have a “thought” component, so don’t classify problems as something to know how to calculate but not understand.


Quick Review of Costs• Different types of costs:

• TC = FC + VC

• FC = Costs that do not vary with quantity

• VC = Costs that do vary with quantity

• MC = cost of one additional unit of production = dTC/dQ

• AC = TC/Q

• Opportunity cost = value of next best opportunity• What else could you be doing with your resources?

• Sunk costs = costs already expended or non-recoverable• Is the cost behind you on the decision tree?


Quick Review of Pricing• Perfectly competitive firm sets P=MC to maximize profits

• Since firms are price takers and can sell as many units as they choose at price P, MR = P for any firm.

• In short-run equilibrium (without entry) firms can be profitable, if AC<MC. If AC=MC then economic profit = 0. If AC>MC then a firm should shut down.

• Monopolist sets MR=MC to maximize profits• Find MR by taking derivative of TR=P(Q)*Q (or if you have a demand

curve of the type P=a-b*Q, remember that MR=a-2b*Q – but really, just do the calculus).

• Revenues are not maximized at the same production point as profits, unless MC=0 (revenues are maximized where MR=0).

• Monopolist therefore produce at an elastic point on the demand curve, unless MC=0, in which case elasticity = -1.

• Remember the steps to find a maximum/minimum from previous slides!


Quick Review of Price Discrimination• Price discrimination allows monopolist to charge different

rates to different consumers.• Only meaningful for a monopoly (Why?)

• If some kind of PD is profitable, it helps the monopolist vs. single price benchmark.

• Ambiguous effect on consumers (some customers previously “shut out” of the market may get to consume).

• 1st degree: charge each consumer its WTP• Not seen very often in real life

• 3rd degree: sort customers based on some observable trait where it’s legal to charge different prices (e.g.: student tickets at movies)


Quick Review of Price Discrimination• 2nd degree PD and its relatives: allow customers to self select

(versioning, intertemporal PD, quantity discounts)– Give customers the incentive to self-select by making their consumer

surplus greatest for the product type you want them to select.


Tips for 2nd Degree PD Problems

1. Set up strategies or a “menu of options” and methodically calculate the prices which get customers to do what you want them to do. Pick the option that maximizes profit.

2. Some options to try:1. Sell one product, only to high valuation group.

2. Sell one product to everyone (note high valuation group will get rent).

3. Set up a 2nd degree PD scheme.

3. General rules for setting up 2nd degree PD scheme:1. Always charge low WTP group its maximum WTP for low quality

product.

2. Make sure that high WTP group buys high quality product by giving more than CS from choosing low quality product.


Long Run vs. Short Run• Short run

• There may be fixed costs; the number of firms is fixed.• Set MR=MC; exit if P<min AVC• May want to stay open if P<ATC

• Long run• No fixed costs, all costs are variable.

• This is definitional; hence “long run” varies by industry.• In long run, P=MC=minAC.

• Firms with AC<MC make positive economic profit enter.• Firms with AC>MC make negative economic profit exit.

• Thought question: why do firms produce if they’re getting 0 profits?


Long Run Equilibrium• Long-run competitive equilibrium (Can refer to P&R, p. 284)

• All firms in industry are maximizing profit.

• No firm has incentive to enter or exit.

• Price of product equates Qs with Qd.

• Occurs where economic profits = 0 and MC = minAC• To get the minimum point on an AC curve, you have 2 options:

• Set MC=AC and solve (since they cross where AC is lowest).• Take dAC/dQ and solve for where this equals 0.


Problem Set #5, Q2• TC=400+q^2 MC=2q and AC=400/q + q

• A) Perfectly competitive market, P=100. How many pencils do you produce?

• Solution approach: set P=MC and solve for q.

• 100=2q q=50, profit=$2100

• B) Market demand: Q=50,000-200P. How many firms are in the market in the short run?

• Solution approach: Find Q, since firms homogenous, we know total firms in market = Q/q

• Q=50,000-200(100)=30,000 Firms = 30,000/50 = 600.


Problem Set #5, Q2 cont.• C) What happens in the long run?

• We know from part A) that firms are making economic profit. In the LR we expect firms to enter to the point where firms make zero profit.

• Solution approach: find where P=minAC

• Approach (1): set MC=AC: 2q=400/q + q q*=20

MC=40 P*=40 Q*=50,000-200(40)=42,000

total number of firms=42,000/20=2100.

• Approach (2): set dAC/dq=0: -400/q^2 + 1 =0 q^2 = 400 q*=20….


Problem Set #5, Q2 cont.• D) One plant with new technology (P=$40 from before)

• TCnew=200+qnew^2/2 MCnew=qnew and ACnew=200/qnew + qnew/2

• Solution approach: set P=MCnew and solve for qnew.• 40=qnew qnew=40, profit (for new firm)=$600.• qnew=40 = 2x20 = 2xqold two old firms replaced.• New number of firms: 2100 (before) – 2 (displaced) + 1 (new) = 2099.

• E) Patent, so now can use technology in multiple plants• Solution approach: build just enough new plants to drive older plants

out of market.• Set AC=MC to minimize costs (lowest part of AC curve) 200/q +

q/2 = q q*=20.• Number plants = 42,000/20 = 2100.• Profit (per plant) = (40)(20) – [200+400/2]=$400.


Problem Set #5, Q3• A) On peak days, we face demand P=1000-Q. TR=P(Q)*Q=1000Q-Q2

MR=1000-2Q.• Solution approach: set MR=MC and solve for Q.• What are our costs? If we have already booked the plane, the $20,000 lease

cost is sunk (if not, it’s a fixed cost), and the operating cost of $30,000 per round-trip flight is also sunk or fixed given that we’ve already decided to make the flight (sunk if we’ve paid for it, fixed if not) (i.e. think of it like the fuel is in the plane, we’re just deciding how much to charge passengers).

• Analogy: if you need to rent a building for a production process, if you only need to produce in one building it’s a fixed cost, if you’re deciding how many buildings to produce in because you might need more room depending on how much you want to produce, it’s a variable cost (varies with quantity produced), and if you’ve already paid for the building it’s a sunk cost.

• So our only marginal cost for flying an additional person is $40/person.


Problem Set #5, Q3 cont.

• A) (cont.) Setting MR = MC, 1000-2Q=40 Q=480. Problem: the plane can only carry 300 people. So carry 300 people – it’s the best you can do. But at what price? You can afford to lose some customers by raising the price: with demand P=1000-Q, P=700.

• On off-peak days, we similarly get: P=400-Q TR=400Q-Q2 MR=400-2Q MR = MC 400-2Q=40 Q=180 P=220.

• B) This question asks us about whether we choose to *operate* the flight. Thus, it presumes we’ve already decided whether to *lease* it. The lease cost is a sunk cost, and now we are only considering whether to operate it.



• B) (cont.) Should we operate? • Solution approach: compare TR and TC to get profit.• Peak days: TR=700*300=210,000,

TC=30,000+40*300=42,000 Profit=168,000• Off-peak days: TR= 220*180=39,600,

TC=30,000+40*180=37,200 Profit=2,400

Operate on both kinds of days since positive profits.



• C) Again, let’s calculate profit, this time taking the cost of the lease into consideration.

• You can solve this question by calculating profits for the whole 6 month period if you prefer; you’ll get the same answer by looking at a 1 week period, though, since the weeks are identical.

• You could also solve this question by calculating e.g. peak days TR = 210,000, TC = 42,000+20,000, etc.

• But as a short cut we can simply write weekly operating profit=2*168,000+4*2,400=345,600 (total revenue net of operation costs), weekly TC of renting = 7*20,000 = 140,000 total profit of $205,600. Either way!



• D) We can make 600 roundtrips! Great! – But is there that much demand?

• We know from part A) that with the demand for off-peak days, we only want to sell 180 tickets on off-peak days. Since operating any one flight has an operating cost associated with it, we want these 180 tickets to be on the same plane.

• We know from part A) that with the demand for peak days, we want to sell 480 tickets on peak days. Our MR and MC stay the same (TR=P(Q)*Q=1000Q-Q2 MR=1000-2Q, MC=40 ($40/person)) we still want to sell 480 tickets, and what will be their price, now that we *can* sell that many tickets? Simply plug back into the demand: P=1000-480=520.

• Percent of capacity used would fall, but so what?



• E) Solution approach: calculate profits for the new option (as before) but also compare to the other option (not leasing the second plane) because you want to make the decision that *maximizes* profits.

• Now that the lease cost isn’t a sunk cost, let’s re-do our profit calculations: Operating profit for a peak day was (480*520)-(2*30,000+480*40)=170,400. Operating profit for a non-peak day was 2,400. Weekly operating profit is 2*170,400+4*2,400=350,400. Weekly lease cost: 2*7*20,000=280,000 Weekly total profit of 70,400.

• But wait! We had higher profits when we only operated one plane (part C). Thus, only lease one plane.


General exam tips

• Pay attention to how much each question is worth and make sure you don’t accidentally skip over a sub-part of a question.

• Explain things clearly, accurately, concisely. (You don’t want to omit an important part of the full answer. On the other hand, if you ramble, the chances might increase that you write something wrong. Give “the truth, the whole truth, and nothing but the truth” .)

• Good luck!

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October 3, 2009Final Exam Review1 EWMBA 201A Eva Vivalt