Instructor Sandeep Basnyat Sandeep_basnyat@yahoo.com 9841 892281 Managerial Economics Ace Institute of Management Executive MBA Program Remainings from Objectives of the Firm Instructor Sandeep Basnyat Sandeep_basnyat@yahoo.com 9841 892281

Profit Maximization If increase Q by one unit, revenue rises by MR, cost rises by MC. If MR > MC, then increase Q to raise profit. If MR < MC, then reduce Q to raise profit. What Q maximizes the firm’s profit?

Firms maximize profit by producing the Quantity until Profit Maximization Q TR TC Profit MR MC Profit = MR – MC At any Q with MR > MC, increasing Q raises profit. $0 45 33 23 15 9 $5 5 7 1 –$5 $10 12 10 8 6 $4 –2 2 4 $6 1 10 10 2 20 At any Q with MR < MC, reducing Q raises profit. 10 3 30 10 4 40 (The table on this slide is similar to Table 2 in the textbook.) For most students, seeing the complete table all at once is too much information. So, the table is animated as follows: Initially, the only columns displayed are the ones students saw at the end of the exercise in Active Learning 1: Q, TR, and MR. Then, TC appears, followed by MC. It might be useful to remind students of the relationship between MC and TC. Then, the Profit column appears. Students should be able to see that, at each value of Q, profit equals TR minus TC. The last column to appear is the change in profit. When the table is complete, we use it to show it is profitable to increase production whenever MR > MC, such as at Q = 0 , 1, or 2. it is profitable to reduce production whenever MC > MR, such as at Q = 5. 10 5 50 Firms maximize profit by producing the Quantity until MR = MC

Exercise Calculate the profit maximizing output (Q); and Assume a cost function: TC = 1000 + 2Q + 0.01Q2 and a constant marginal revenue $10 per unit for a firm. Calculate the profit maximizing output (Q); and Total profit if the selling price per unit (P) = MR. Solution: a) MC = dTC /dQ = 2+0.02Q Profit maximizing output is at where MR = MC 10 = 2+0.02Q Therefore, Profit Maximizing Quantity (Q) = 400 units. b) Profit = TR –TC = [(PxQ) – TC] = [(10x400) – (1000 + 2(400) + 0.01(4002)] = $600

Exercise Assume the following functions for a firm Demand : Q = 90 – 2P Total Revenue: TC = Q3 - 8Q2 + 57Q + 2 Find the followings for this firm. Profit maximizing Quantity Price per unit Total Profit Q = 4 P = 43 π = 6

Sales Revenue or Revenue Maximization Q P TR AR MR Sales Revenue Maximization Condition MR = 0 $4.50 9 10 7 4 $ 0 n.a. 1 4.00 1.50 2.00 2.50 3.00 3.50 $4.00 –1 1 2 3 $4 2 3.50 3 3.00 4 2.50 When the AR column appears, note that AR = P at every quantity. This, of course, is a tautology. When the MR column appears, note that MR is less than P. This is not as easy to see, because the MR numbers are offset from the rows of the table, just as if you were in an elevator stuck between two floors. But students can still see that MR < P. For example, in the range of output of Q=2 to Q=3, the price ranges from $3.50 to $3.00, but MR is only $2. 5 2.00 6 1.50

Exercise Assume the following functions for a firm Demand : P = 7,500 – 3.75Q Total Cost: TC = 1,012,500 + 1,500Q + 1.25Q2 Find the followings for this firm. Revenue maximizing Quantity Price per unit Total Revenue Total Profit / Loss Q = 1000 units. P = 3,750 TR = 3,750,000 π = - 12,500

Exercise Profit Revenue 90 100 i) Maximizing Quantity 2200 2000 Assume the following functions for a firm Demand : P = 4,000 – 20Q Total Cost: TC = 2000 + 400Q Find the followings for this firm under Profit maximization objective Revenue Maximization objective. Profit Revenue 90 100 2200 2000 1,60,000 1,58,000 i) Maximizing Quantity ii) Price per unit iii) Total Profit / Loss

Numerical Exercise Assume the following functions for a firm: Demand : P = 20 – Q Total Cost: TC = Q2 + 8Q + 2 a) Find Price (P), Quantity (Q) and Total Profit (or Loss) for each of the following conditions: Profit maximization Revenue Maximization b) Find Price (P), Quantity (Q), Total Revenue (TR) and Total cost (TC) for sales maximization with profit constraint or profit constraint of 8 or higher. P = 17, Q = 3, π = 16 P = 10, Q = 10, π = 82 (loss) When Q = 1; P = 19, TR = 19, TC = 11 When Q = 5; P = 15, TR = 75, TC = 67 Firm should produce Q = 5.

Average Total Cost or Average Cost Minimization Related to two important costs: MC and ATC Recall: ATC = AFC + AVC or TC / Q MC = ∆TC ∆Q

Marginal Cost ∆TC MC = ∆Q Marginal Cost (MC) is the change in total cost from producing one more unit: $100 $70 1 170 ∆TC ∆Q MC = 50 2 220 40 3 260 50 4 310 70 5 380 100 6 480 140 7 620

Average Total Cost Curves $0 $25 $50 $75 $100 $125 $150 $175 $200 1 2 3 4 5 6 7 Q Costs Q TC ATC $100 n.a. 1 170 $170 2 220 110 3 260 86.67 4 310 77.50 5 380 76 6 480 80 7 620 88.57

Important Economic Relation: ATC and MC When MC < ATC, ATC is falling. When MC > ATC, ATC is rising. The MC curve crosses the ATC curve at the ATC curve’s minimum. $0 $25 $50 $75 $100 $125 $150 $175 $200 1 2 3 4 5 6 7 Q Costs ATC MC The textbook gives a nice analogy to help students understand this. A student’s GPA is like ATC. The grade she earns in her next course is like MC. If her next grade (MC) is less than her GPA (ATC), then her GPA will fall. If her next grade (MC) is greater than her GPA (ATC), then her GPA will rise. I suggest letting students read the GPA example in the book, and giving them the following example in class: You run a pizza joint. You’re producing 100 pizzas per night, and your cost per pizza (ATC) is $3. The cost of producing one more pizza (MC) is $2. If you produce this pizza, what happens to ATC? Most students will understand immediately that ATC falls (albeit by a small amount). Instead, suppose the cost of producing one more pizza (MC) is $4. Then, producing this additional pizza causes ATC to rise. ATC is minimum where, ATC = MC AVC is minimum where, AVC = MC

Exercise Given the cost function: TC = 1000 + 10Q - 0.9Q2 + 0.04Q3 Find Q when AVC is minimum. Solution When AVC is minimum: AVC = MC 10 - 0.9Q + 0.04Q2 = 10-1.8Q+ 0.12Q2 Or, - 0.08Q2 + 0.9Q = 0 Or, Q(- 0.08Q+ 0.9) = 0 Or, Q =0 and - 0.08Q+ 0.9 = 0 i.e, Q = 11.25 (Minimum AVC)

Exercise Assume the following functions for a firm Demand : P = 7,500 – 3.75Q Total Cost: TC = 1,012,500 + 1,500Q + 1.25Q2 Find the followings for this firm if your objective is to minimize average cost. a) Q b) Price per unit c) Total Revenue d) Total Profit Q = 900 P = 4,125 TR = 3,712,500 π = 337,500

Instructor Sandeep Basnyat Sandeep_basnyat@yahoo.com 9841 892281 Managerial Economics Ace Institute of Management Executive MBA Program Session 2: Supply, Demand and Elasticity Instructor Sandeep Basnyat Sandeep_basnyat@yahoo.com 9841 892281

Demand Demand comes from the behavior of buyers. Demand comes from the behavior of buyers. The quantity demanded of any good is the amount of the good that buyers are willing and able to purchase. Law of demand: the claim that the quantity demanded of a good falls when the price of the good rises, other things equal.

The Market Demand Curve for Orange P Qd (Market) $0.00 24 1.00 21 2.00 18 3.00 15 4.00 12 5.00 9 6.00 6 P Q

Demand Curve Shifters: Non-price Determinants of Demand Price Number of buyers Income level Effect on normal goods Effect on inferior good Prices of other goods Substitute goods Complement goods Taste or Preference Expectation Qty Price Qty

Q = 10,000 – 200 P + 0.03POp + 0.6I + 0.2 A Numerical exercise The ABC Marketing consulting firm found that a particular brand of portable stereo has the following demand curve for a certain region: Q = 10,000 – 200 P + 0.03POp + 0.6I + 0.2 A Where, Q = quantity per month P = Price in $ Pop = Population I = Disposable income A = Advertising expenditure in $ Determine the demand curve for the company in a market in which P = 300, Pop = 1,000,000, I = 30,000, and A = 15000 b) Calculate the quantity demanded at prices of $200 c) Calculate the price necessary to sell 45,000 units. (Ans.: Q = 61,000 – 200P) (Ans.: 21000) (Ans.: $80)

Supply Supply comes from the behavior of sellers. Supply comes from the behavior of sellers. The quantity supplied of any good is the amount that sellers are willing and able to sell. Law of supply: the claim that the quantity supplied of a good rises when the price of the good rises, other things equal

Market Supply Schedule & Curve Market Supply Schedule & Curve Price of lattes Quantity of lattes supplied $0.00 1.00 3 2.00 6 3.00 9 4.00 12 5.00 15 6.00 18 P Q

Shift supply curve left or right Supply Curve Shifters Shift supply curve left or right Number of sellers Input prices Technology Expectation Again, the animation here is carefully designed to help make clear that a shift in the supply curve means that there is a change in the quantity supplied at each possible price. If it seems tedious, you can turn it off. In any case, be assured that, by the end of this chapter, the animation of curve shifts will be streamlined and simplified.

Supply and Demand Together Supply and Demand Together P Q Equilibrium Price and Quantity S D We now return to the latte example to illustrate the concepts of equilibrium, shortage and surplus.

Numerical Problem on Demand and Supply 1) Suppose: Demand eqn. for a product: Qd = 286 − 20p Supply eqn. For a product: Qs = 88 + 40p Find Equilibrium Quantity and Price: Solution: Qd = Qs 286 − 20p = 88 + 40p 60p = 198 P = $3.30 Q = 286 – 20(3.3) = 220

Comparative Static Analysis Sensitivity analysis or “what-if” analysis. The role of factors influencing demand is analyzed while holding supply conditions constant. Or, the role of factors influencing supply is analyzed by studying changes in supply while holding demand conditions constant Short and Long run analyses Short: Price adjustment to stabilize equilibrium Long: Reallocation of resources

when quantity supplied is greater than quantity demanded Surplus: when quantity supplied is greater than quantity demanded P Q Example: If P = $5, S D Surplus then QD = 9 and QS = 25 resulting in a surplus of 16 units

Short-run market change: Rationing Mechanism of Price: Surplus case P Q Facing a surplus, sellers try to increase sales by cutting the price. S D Surplus This causes QD to rise and QS to fall… …which reduces the surplus.

Short-run market change: Rationing Mechanism of Price: Surplus case P Q Facing a surplus, sellers try to increase sales by cutting the price. S D Surplus Falling prices cause QD to rise and QS to fall. Prices continue to fall until market reaches equilibrium.

What happens if the market price is lower than equilibrium price? Shortage What happens if the market price is lower than equilibrium price? P Q Example: If P = $1, S D then QD = 21 lattes and QS = 5 lattes resulting in a shortage of 16 lattes Shortage

Short-run market change: Rationing Mechanism of Price: Shortage case P Q Facing a shortage, sellers raise the price, S D causing QD to fall and QS to rise, …which reduces the shortage. Shortage

Short-run market change: Rationing Mechanism of Price: Shortage case Facing a shortage, sellers raise the price, P Q causing QD to fall S D and QS to rise. Prices continue to rise until market reaches equilibrium. Rationing Mechanism: Price adjustment to balance demand and supply in market Shortage

Long run analysis: Guiding or Allocating Mechanism: Market for Hybrid Cars EVENTS: 1. Price of gas rises 2.New technology reduces production costs P Q S1 S2 D2 D1 P2 P3 Q3 Short-run Analysis P1 Q1 Long-run Analysis Q2

Increase in D> Increase in S. What about others? P Q P Q S1 S2 S1 S2 D2 D2 D1 D1 P2 P3 Q3 P1 Q1 P1 Q1 P2 Q2 Q2

Elasticity and its application

Price Elasticity of Demand Price elasticity of demand = Percentage change in Qd Percentage change in P Price elasticity of demand measures how much Qd responds to a change in P.

Price Elasticity of Demand Price elasticity of demand = Percentage change in Qd Percentage change in P P Q Example: D P rises by 10% Price elasticity of demand equals P2 Q2 P1 Q1 15% 10% = 1.5 Q falls by 15% What does elasticity = 1.5 mean?

Calculating Percentage Changes Standard method of computing the percentage (%) change: Calculate Price Elasticity of Demand end value – start value start value x 100% P Q 2500 10 B D 2000 15 A

Calculating Percentage Changes Demand for your guiding Problem: From A to B, P rises 25%, Q falls 33.33%, elasticity = 33.33/25 = -1.33 From B to A, P falls 20%, Q rises 50%, elasticity = 50/20 = - 2.50 P Q 2500 10 B D 2000 15 A How to solve this confusion?

Calculating Percentage Changes So, we instead use the midpoint method: end value – start value midpoint x 100% The midpoint is the number halfway between the start & end values, also the average of those values. It doesn’t matter which value you use as the “start” and which as the “end” – you get the same answer either way! What is PED using midpoint method?

Calculating Percentage Changes Using the midpoint method, the % change in P equals 2500 – 2000 2250 x 100% = 22.2% The % change in Q equals 10 – 15 12.5 x 100% = - 40.0% These calculations are based on the example shown a few slides back: points A and B on the website demand curve. The price elasticity of demand equals 40/22.2 = - 1.8

A C T I V E L E A R N I N G 1: Calculate an elasticity Use the following information to calculate the price elasticity of demand for hotel rooms using midpoint method: if P = $70, Qd = 5000 if P = $90, Qd = 3000 42

A C T I V E L E A R N I N G 1: Answers Use midpoint method to calculate % change in Qd (5000 – 3000)/4000 = 50% % change in P ($70 – $90)/$80 = - 25% The price elasticity of demand equals 50% 25% = - 2.0 43

Calculating Price Elasticity of Demand

Numerical example Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows: Price($) Demand (millions) 60 22 80 20 100 18 120 16 Calculate the price elasticity of demand when the price is $80.

Solution to Numerical example From the above question, with each price increase of $20, the quantity demanded decreases by 2. Therefore, At P = 80, quantity demanded equals 20 and

Calculating Price Elasticity of Demand The estimated linear demand function for pork is: Q = 286 -20p where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year. At the equilibrium point of p = $3.30 and Q = 220 Find the elasticity of demand for pork:

Calculating Price Elasticity of Demand The estimated linear demand function for pork is: Q = 286 -20p where Q is the quantity of pork demanded in million kg per year and p is the price of pork in $ per year. At the equilibrium point of p = $3.30 and Q = 220 the elasticity of demand for pork:

Numerical Example Demand for a publisher’s book is given as: Qx = 12,000 – 5,000Px + 5I + 500Pc Px = Price of the book = $5 I = Income per capita = $10,000 Pc = Price of the books from competing publishers = $6 Find Price elasticity of demand for the book.

Solution to Numerical Example Substituting the values of I and Pc Qx = 12,000 – 5,000Px + 5(10000) + 500(6) Or, Qx = 65,000 – 5,000Px When Px = $5 (given), Qx = 40,000 Now, dQx/dPx = - 5000 Therefore, E p = -5000 x (5 / 40000) = - 0.625

The Determinants of Price Elasticity The price elasticity of demand depends on: the extent to which close substitutes are available whether the good is a necessity or a luxury how broadly or narrowly the good is defined the time horizon: elasticity is higher in the long run than the short run. This slide is a convenience for your students, and replicates a similar table from the text. If you’re pressed for time, it is probably safe to omit this slide from your presentation.

The Variety of Demand Curves Economists classify demand curves according to their elasticity. The price elasticity of demand is closely related to the slope of the demand curve. Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity. The next 5 slides present the different classifications, from least to most elastic.

“Perfectly inelastic demand” (one extreme case) Price elasticity of demand = % change in Q % change in P 0% = 0 10% D curve: P Q D vertical Q1 P1 Consumers’ price sensitivity: P2 If Q doesn’t change, then the percentage change in Q equals zero, and thus elasticity equals zero. It is hard to think of a good for which the price elasticity of demand is literally zero. Take insulin, for example. A sufficiently large price increase would probably reduce demand for insulin a little, particularly among people with very low incomes and no health insurance. However, if elasticity is very close to zero, then the demand curve is almost vertical. In such cases, the convenience of modeling demand as perfectly inelastic probably outweighs the cost of being slightly inaccurate. P falls by 10% Elasticity: Q changes by 0%

Price elasticity of demand “Inelastic demand” Price elasticity of demand = % change in Q % change in P < 10% < 1 10% D D curve: P Q relatively steep Q1 P1 Consumers’ price sensitivity: P2 Q2 relatively low An example: student demand for textbooks that their professors have required for their courses. Here, it’s a little more clear that elasticity would be small, but not zero. At a high enough price, some students will not buy their books, but instead will share with a friend, or try to find them in the library, or just take copious notes in class. Another example: gasoline in the short run. P falls by 10% Elasticity: < 1 Q rises less than 10%

Price elasticity of demand “Unit elastic demand” Price elasticity of demand = % change in Q % change in P 10% = 1 10% D D curve: P Q intermediate slope Q1 P1 Consumers’ price sensitivity: P2 Q2 intermediate This is the intermediate case: the demand curve is neither relatively steep nor relatively flat. Buyers are neither relatively price-sensitive nor relatively insensitive to price. This is also the case where price changes have no effect on revenue. P falls by 10% Elasticity: 1 Q rises by 10%

Price elasticity of demand “Elastic demand” Price elasticity of demand = % change in Q % change in P > 10% > 1 10% D D curve: P Q relatively flat Q1 P1 Consumers’ price sensitivity: P2 Q2 relatively high A good example here would be Rice Krispies, or nearly anything with readily available substitutes. An elastic demand curve is flatter than a unit elastic demand curve (which itself is flatter than an inelastic demand curve). P falls by 10% Elasticity: > 1 Q rises more than 10%

“Perfectly elastic demand” (the other extreme) Price elasticity of demand = % change in Q % change in P any % = infinity 0% D curve: P Q horizontal P2 = P1 D Consumers’ price sensitivity: Q1 Q2 extreme “Extreme price sensitivity” means the tiniest price increase causes demand to fall to zero. “Q changes by any %” – when the D curve is horizontal, the quantity is indeterminant. Consumers might demand Q1 units one month, Q2 units another month, and some other quantity later. Q can change by any amount, but P always “changes by 0%” (i.e. doesn’t change). If perfectly inelastic is one extreme, this (perfectly elastic) is the other. Here’s a good real-world example of a perfectly elastic demand curve, which foreshadows an upcoming chapter on firms in competitive markets. Suppose you run a small family farm in Iowa. Your main crop is wheat. The demand curve in this market is downward-sloping, and the market demand and supply curves determine the price of wheat. Suppose that price is $5/bushel. Now consider the demand curve facing you, the individual wheat farmer. If you charge a price of $5, you can sell as much or as little as you want. If you charge a price even just a little higher than $5, demand for YOUR wheat will fall to zero: Buyers would not be willing to pay you more than $5 when they could get the same wheat elsewhere for $5. Similarly, if you drop your price below $5, then demand for YOUR wheat will become enormous (not literally infinite, but “almost infinite”): if other wheat farmers are charging $5 and you charge less, then EVERY buyer will want to buy wheat from you. Why is the demand curve facing an individual producer perfectly elastic? Recall that elasticity is greater when lots of close substitutes are available. In this case, you are selling a product that has many perfect substitutes: the wheat sold by every other farmer is a perfect substitute for the wheat you sell. P changes by 0% Elasticity: infinity Q changes by any %

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