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Managerial Economics Ace Institute of Management Executive MBA Program Remainings from Objectives of the Firm Instructor Sandeep Basnyat

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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?

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Profit Maximization $5$00 Profit = MR – MC MCMRProfitTCTRQ At any Q with MR > MC, increasing Q raises profit –$5 10 – $ $4$10 At any Q with MR < MC, reducing Q raises profit. Firms maximize profit by producing the Quantity until MR = MC

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

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Exercise Assume the following functions for a firm Demand : Q = 90 – 2P Total Revenue: TC = Q 3 - 8Q Q + 2 Find the followings for this firm. a)Profit maximizing Quantity b)Price per unit c)Total Profit Q = 4 P = 43 π = 6

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$ n.a $ 0$4.500 MRARTRPQ – $4 Sales Revenue or Revenue Maximization Sales Revenue Maximization Condition MR = 0

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Exercise Assume the following functions for a firm Demand : P = 7,500 – 3.75Q Total Cost: TC = 1,012, ,500Q Q 2 Find the followings for this firm. Q = 1000 units. a)Revenue maximizing Quantity b)Price per unit c)Total Revenue d)Total Profit / Loss P = 3,750 TR = 3,750,000 π = - 12,500

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Exercise Assume the following functions for a firm Demand : P = 4,000 – 20Q Total Cost: TC = Q Find the followings for this firm under (a)Profit maximization objective (b)Revenue Maximization objective. i) Maximizing Quantity ii) Price per unit iii) Total Profit / Loss ProfitRevenue ,60,0001,58,000

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Numerical Exercise Assume the following functions for a firm: Demand : P = 20 – Q Total Cost: TC = Q 2 + 8Q + 2 a) Find Price (P), Quantity (Q) and Total Profit (or Loss) for each of the following conditions: i)Profit maximization ii)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.

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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∆Q

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Marginal Cost (MC) is the change in total cost from producing one more unit: Marginal Cost $1000 MCTCQ $70 ∆TC ∆Q∆Q MC =

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$0 $25 $50 $75 $100 $125 $150 $175 $ Q Costs Average Total Cost Curves $170 n.a. ATC $1000 TCQ

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Important Economic Relation: ATC and MC ATC MC $0 $25 $50 $75 $100 $125 $150 $175 $ Q Costs 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. ATC is minimum where, ATC = MC AVC is minimum where, AVC = MC

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Exercise Given the cost function: TC = Q - 0.9Q Q 3 Find Q when AVC is minimum. Solution When AVC is minimum: AVC = MC Q Q 2 = Q+ 0.12Q 2 Or, Q Q = 0 Or, Q(- 0.08Q+ 0.9)= 0 Or, Q =0 and Q+ 0.9 = 0 i.e, Q = (Minimum AVC )

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Exercise Assume the following functions for a firm Demand : P = 7,500 – 3.75Q Total Cost: TC = 1,012, ,500Q Q 2 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 P = 4,125 TR = 3,712,500 π = 337,500 Q = 900

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Managerial Economics Ace Institute of Management Executive MBA Program Session 2: Supply, Demand and Elasticity Instructor Sandeep Basnyat

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Demand 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.

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P Q The Market Demand Curve for Orange P Q d (Market) $

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Demand Curve Shifters: Non-price Determinants of Demand 1.Number of buyers 2.Income level a.Effect on normal goods b.Effect on inferior good 3.Prices of other goods a.Substitute goods b.Complement goods 4.Taste or Preference 5.Expectation Price Qty Price Qty

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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 POp + 0.6I A Where, Q = quantity per month P = Price in $ Pop = Population I = Disposable income A = Advertising expenditure in $ a)Determine the demand curve for the company in a market in which P = 300, Pop = 1,000,000, I = 30,000, and A = b) Calculate the quantity demanded at prices of $200 c) Calculate the price necessary to sell 45,000 units. Numerical exercise (Ans.: Q = 61,000 – 200P) (Ans.: 21000) (Ans.: $80)

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Supply 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

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Market Supply Schedule & Curve Price of lattes Quantity of lattes supplied $ P Q

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Supply Curve Shifters 1.Number of sellers 2.Input prices 3.Technology 4.Expectation Shift supply curve left or right

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P Q Supply and Demand Together D S Equilibrium Price and Quantity

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

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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

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

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

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

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

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

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

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Long run analysis: Guiding or Allocating Mechanism: Market for Hybrid Cars P Q D1D1 S1S1 P1P1 Q1Q1 S2S2 D2D2 P3P3 Q3Q3 EVENTS: 1. Price of gas rises 2.New technology reduces production costs P2P2 Q2Q2 Short-run Analysis Long-run Analysis

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Increase in D> Increase in S. What about others? P Q D1D1 S1S1 P1P1 Q1Q1 S2S2 D2D2 P3P3 Q3Q3 P2P2 Q2Q2 P Q D1D1 S1S1 P1P1 Q1Q1 S2S2 D2D2 P2P2 Q2Q2

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Elasticity and its application

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

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Price Elasticity of Demand Price elasticity of demand equals P Q D Q2Q2 P2P2 P1P1 Q1Q1 P rises by 10% Q falls by 15% 15% 10% = 1.5 Price elasticity of demand = Percentage change in Q d Percentage change in P Example: What does elasticity = 1.5 mean?

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

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

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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?

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Calculating Percentage Changes Using the midpoint method, the % change in P equals 2500 – x 100% = 22.2% The % change in Q equals 10 – x 100% = % The price elasticity of demand equals 40/22.2 = - 1.8

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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, Q d = 5000 if P = $90, Q d =

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

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Calculating Price Elasticity of Demand

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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) Calculate the price elasticity of demand when the price is $80.

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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

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Calculating Price Elasticity of Demand The estimated linear demand function for pork is: Q = p ◦ 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:

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Calculating Price Elasticity of Demand The estimated linear demand function for pork is: Q = p ◦ 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:

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

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Solution to Numerical Example Solution: a)Substituting the values of I and P c Q x = 12,000 – 5,000P x + 5(10000) + 500(6) Or, Q x = 65,000 – 5,000P x When P x = $5 (given), Q x = 40,000 Now, dQ x /dP x = Therefore, E p = x (5 / 40000) =

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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. 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.

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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.

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Q1Q1 P1P1 D “Perfectly inelastic demand” (one extreme case) P Q P2P2 P falls by 10% Q changes by 0% 0% 10% = 0 Price elasticity of demand = % change in Q % change in P = Consumers’ price sensitivity: D curve: Elasticity: vertical 0 0

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D “Inelastic demand” P Q Q1Q1 P1P1 Q2Q2 P2P2 Q rises less than 10% < 10% 10% < 1 Price elasticity of demand = % change in Q % change in P = P falls by 10% Consumers’ price sensitivity: D curve: Elasticity: relatively steep relatively low < 1

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D “Unit elastic demand” P Q Q1Q1 P1P1 Q2Q2 P2P2 Q rises by 10% 10% = 1 Price elasticity of demand = % change in Q % change in P = P falls by 10% Consumers’ price sensitivity: Elasticity: intermediate 1 D curve: intermediate slope

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D “Elastic demand” P Q Q1Q1 P1P1 Q2Q2 P2P2 Q rises more than 10% > 10% 10% > 1 Price elasticity of demand = % change in Q % change in P = P falls by 10% Consumers’ price sensitivity: D curve: Elasticity: relatively flat relatively high > 1

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D “Perfectly elastic demand” (the other extreme) P Q P1P1 Q1Q1 P changes by 0% Q changes by any % any % 0% = infinity Q2Q2 P 2 = Consumers’ price sensitivity: D curve: Elasticity: infinity horizontal extreme Price elasticity of demand = % change in Q % change in P =

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