demand - Managerial Economics Examples from Lecture Demand...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Managerial Economics Examples from Lecture Demand and Profit Maximization 1 Example 1: Maximizing Profit with Linear Demand Suppose inverse demand is 10 0.1 p q =- . Revenue is (10 0.1 ) R pq q q = =- , assuming a constant unit price Suppose fixed cost is $5 per unit and costs are a constant $2 per unit, or ( ) 5 2 C q q = + Profit is (10 0.1 ) 2 5 R C q q q =- =--- . To maximize profit: (10 0.1 ) 0.1 2 8 0.2 8 0.2 8/0.2 40 d q q dq q q q =--- =- = = = = Substituting gives: 10 0.1(40) 6 6 40 2 40 5 155 p =- = =-- = i i . Suppose instead you had been given demand, not inverse demand. Demand can be found by rearranging the inverse demand curve given. 10 0.1 0.1 10 (10 )/0.1 100 10 p q q p q p q p =- =- =- =- Revenue and profit are: (100 10 ) R pq p p = =- (100 10 ) 2(100 10 ) 5 R C p p p =- =---- Maximizing: (100 10 ) 10 2( 10) 120 20 120 20 6 : 100 10(6) 40 6(40) 2(40) 5 155 d p p dp p p p Substituting q =---- =- = = = =- = =-- = Suppose instead Revenue is maximized. Using the inverse demand: (10 0.1 ) 0.1 10 0.2 10 0.2 10/ 0.2 50 10 0.1(50) 5 5(50) 250 6(40) 240 5(50) 2(50) 5 145 155 dR q q dq q q q p R =-- =- = = = = =- = = = > = =-- = < Managerial Economics Examples from Lecture Demand and Profit Maximization 2 Example 2: Maximizing Profit with Log Linear Demand Suppose demand is 3 10000 q p- = and unit cost is constant at $4 per unit. 3 3 2 3 3 4 3 3 4 3 3 4 4 3 (10000 ) 4(10000 ) 10000 40000 : 10000 ( 4) 10000( 3 ( 4) ) 3 ( 4) 3 12 12 2 p p p F p p F OR p p F d p p p dp p p p p p p p p -------------- =-- =-- =-- =-- + = =- =- = Now, divide both sides by 2 and by p-4 to get 3 6 10000(6 ) 46.3 (6 4)(46.3) p q F - = = -- Example 3: Demand for Infrequently Purchased Goods with Unlimited Capacity Of 1000 potential customers, the fraction purchasing is approximated by ( ) 1 0.1 f p p = - and constant unit cost is $2. and constant unit cost is $2....
View Full Document

This note was uploaded on 04/21/2008 for the course ECP 3703 taught by Professor Dewey during the Spring '08 term at University of Florida.

Page1 / 5

demand - Managerial Economics Examples from Lecture Demand...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online