Lecture 5- Partial Derivatives & BCG Matrix.pptx

AGRB 3190: Agribusiness Management Spring 2024 Lecture 5: Elasticities Using Partial Derivatives & BCG Matrix Review: Own Price Elasticity Classifications: Classifications of Own Price Elasticity of Demand: Inelastic demand ( |ED| < 1 ): a change in price brings about a relatively smaller chang...

AGRB 3190: Agribusiness Management Spring 2024 Lecture 5: Elasticities Using Partial Derivatives & BCG Matrix Review: Own Price Elasticity Classifications: Classifications of Own Price Elasticity of Demand: Inelastic demand ( |ED| < 1 ): a change in price brings about a relatively smaller change in quantity demanded (ex. medicine).  Total Revenue = P×Q rises as a result of a price increase Unitary elastic demand ( |ED| = 1 ): a change in price brings about an equivalent change in quantity demanded.  TR= P×Q remains the same as a result of a price increase Elastic demand ( |ED| > 1 ): a change in price brings about a relatively larger change in quantity demanded (ex. expensive wine).  TR = P×Q falls as a result of a price increase 2 3 Example: In episode 20, season 11 of Family Guy the Griffins leave Quahog to become farmers. Assume that they decided to produce tomatoes and the demand function is given by: Q = 60,000 – 5,000P  If the selling price is $8 are we on the elastic or inelastic part? 4 Example: First, we need to find an expression for demand elasticity: ε= If P = 8, Q = 20,000 ε=-2 5 Today:  Partial derivatives!  Income – Cross Price elasticities  Boston Consulting Group Growth Share Matrix 6 The problem is…  That the demand function includes more than the price and quantity demanded. For example: It may include income, prices of other goods etc. How do we find the elasticity then?  Partial derivatives! 7 Partial Derivative  The rules for determining the partial derivatives are the same as those for the “simple” with the assumption that all variables except the one with respect to which the derivative is being taken remain unchanged 8 Example:  Assume that z= f(x,y)= X3y Calculate the partial derivative of z w.r.t. x and y 9 Example:  Assume that z= f(x,y)= X4y3 +8x2y + y4 + 5x Calculate the partial derivative of z w.r.t. x and y 10 Calculating the ED from a demand function  Assume that the demand for beer is given by: Qb = 100 – 30 Pb – 20 Pc + .005I, where Pb is the price of beer (=$5) Pc is the price of a pack of chips (=$1) and I is the annual income (=$25,000). Is the demand for beer elastic? Inelastic? Unitary Elastic? 11 Calculating the ED from a demand function  We need to estimate the partial derivative of the demand function with respect to price of beer 12 Cross Price Elasticity of Demand  Shows the percentage change in quantity demanded of good Y in response to a change in the price of good X  Algebraically: 13 Example:  Assume that the demand for beer is given by: Qb = 100 – 30 Pb – 20 Pc + .005I, where Pb is the price of beer (=$5) Pc is the price of a pack of chips (=$1) and I is the annual income (=$25,000). Calculate the cross price elasticity of demand for beer with respect to the price of chips. 14 Example:  We need to take the partial derivative of the demand function of beer with respect to price of chips  Thus, a one percent increase in price of chips results in a 0.36% decrease in quantity demanded of beer 15 Classification  If (E > 0): implies that as the price of good X increases, the quantity demanded of Good Y also increases. Thus, Y and X are substitutes in consumption (ex. chicken and pork). dyx  If (E < 0): implies that as the price of good X increases, the quantity demanded of Good Y decreases. Thus Y & X are Complements in consumption (ex. beer and chips). dyx  If (E = 0): implies that the price of good X has no effect on quantity demanded of Good Y. Thus, Y & X are Independent in consumption (ex. bread and coke) dyx 16 Example Assume that Joey Tribbiani wants to create and sell a new game called “Bamboozle”. However, before he makes his decision wants to examine whether “Bamboozle” is a competitor for his “ultimate fireball”. The weekly demand equations are: Q1 (P1,P2) = 8,000 – 0.09P12 + 0.08P22 (Bamboozle) Q2 (P1,P2) = 15,000 + 0.04P12 – 0.03 P22 (Ultimate fireball) 17 Example In order to answer Joey’s question we need to take the partial derivative of Q1 with respect to P2 and the partial derivative of Q2 with respect to P1. > 0, >0 So the two products are competitive. 18 Income Elasticity  Shows the percentage change in the quantity demanded of good Y in response to a percentage change in income  Algebraically: 19 Example:  Assume that the demand for beer is given by: Qb = 100 – 30 Pb – 20 Pc + .005I, where Pb is the price of beer (=$5) Pc is the price of a pack of chips (=$1) and I is the annual income (=$25,000). Calculate the income elasticity 20 Example:  We need to estimate the partial derivative of the demand function with respect to income and then substitute the values for Q and I  If income increases by 1% then the quantity demanded of beer will increase by 2.27% 21 Boston Consulting Group Matrix (BCG Matrix)  Created in late 1960s (1968) by the Boston Consulting group  It is still a very popular tool across businesses  Classifies strategic businesses units (SBUs) or products according to growth and market share 22 Strategic Business Unit (SBU) An SBU is defined as a unit that stands alone from the rest of the firm, has its own competitors and its own manager, and is responsible for strategic planning and profits. An SBU can be a company division, a product line within a division or even a single product or brand. Once SBUs are identified, management assesses their attractiveness and decides how much support each one deserves. 23 Boston Consulting Group Matrix (BCG Matrix)  Question Marks  Stars  Cash Cows  Dogs 24 Stars  High growth, high market share  Require a lot of investment to maintain the market share  Lead to large amount of cash consumption and generation  Over time market share declines and SBUs become “cash cows” 25 Cash Cow  Low growth, high market share  Stars of yesterday – foundations of the company  Generate more cash than required  Generate profit by investing the minimum possible amount  Indicate that the industry is mature not growing or declining 26 Question Marks  High growth, low market share  This is the starting point for most companies  Have the potential to become a star but also can become a “dog”  Requires a lot of spending to maintain and increase market share 27 Dogs  Low growth, low market share  Generate enough cash to maintain the SBU  But without the potential to bring in a lot of cash  Business is situated in a decline stage 28 Boston Consulting Group Matrix (BCG Matrix) 29 Classification: If EI > 0, then the good is considered a normal good (ex. beef). If EI < 0, then the good is considered an inferior good (ex. ramen noodles) High income elasticity of demand for luxury goods Low income elasticity of demand for necessary goods 30 Creating Advantage  Sunk Cost effect  Replacement effect 31