# The willingness and ability to buy

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The willingness and ability to buy
Demand The willingness and ability to buy Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Demand learning objectives
Students should be able to Describe and apply demand function and demand curve Distinguish between change in quantity demanded and change in demand Calculate and interpret demand elasticity Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, Chapter 4
Demand Function A mathematical representation of the relationship between the quantity demanded and all factors influencing demand: Q = f(X1, X2,… Xn) where Q is quantity demanded and the Xis are the factors influencing demand Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, Chapter 4
Demand for PTC Tickets Q = P Ps - 3.3Pr I where P is PTC ticket price, Ps is price of symphony tickets, Pr is price of nearby restaurant meals, and I is average per capita income. (Interpret each term of the above equation.) Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, Chapter 4
Variable values Suppose the variables have the following values: P = \$30 Ps = \$50 Pr = \$40 I = \$50,000 How many tickets will PTC sell? Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, Chapter 4
The demand curve Substitute variable values (except for P) into the equation and simplify: P = Q This is the equation for the demand curve. Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Graphing the demand curve
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, Chapter 4
Demand elasticity The price elasticity of demand is given by [Note: the convention used here is to express the elasticity as a negative quantity so that, when calculated, the result is a positive number] Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Calculating elasticity arc price elasticity
Information requirements: Quantity demanded before and after the price change Q1 Q2 Price before and after the price change P1 P2 Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Calculating elasticity arc price elasticity
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Arc price elasticity example
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Calculating elasticity point price elasticity
Information requirements Demand curve equation: Q=a+bP, b=Q/P, b<0 Current price and quantity P Q Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Calculating elasticity point price elasticity
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Point price elasticity example
If the demand equation is Q= P, P=35*, and Q=167, then elasticity is *This price is midway between the two prices in the arc elasticity calculation. Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Range of price elasticities
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Determinants of price elasticity
Availability of substitutes few substitutes for milk many substitutes for milk at the supermarket Size of good in consumer budget consider salt versus a Lexus Time period for consumer adjustment given enough time, how do we adjust to higher fuel prices? Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Price changes and total revenue
PTC’s total revenue is TR=PQ  The inverse demand curve is P=60-.15Q   Substituting, TR=(60-.15Q)Q=60Q-.15Q2   From this we can derive marginal revenue  (MR=TR/Q=60-.30Q) (Well, OK, we did use a little calculus for that last step. Trust us.) Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Elasticity, prices, and total revenue
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Demand, total revenue, & marginal revenue linear demand curve
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Other demand influences
Complements versus substitutes Cross price elasticity of demand Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Other demand influences
Income Normal goods Inferior goods Income elasticity Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Managerial Economics and Organizational Architecture, Chapter 4
Product life cycle Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Omitted variables problem
1998 1999 2000 Income (I) \$3,000 \$4,000 \$3,500 Advertising (A) 2 3 2.5 Price (P) 10 Sales (S) 236 284 260 True demand S=120-2P+8A+0.04I Estimated demand S=140+48A Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

Estimating demand the identification problem
Managerial Economics and Organizational Architecture, Chapter 4 McGraw-Hill/Irwin

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