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demand - Managerial Economics Examples from Lecture...

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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 π = - = - - - . To maximize profit: (10 0.1 ) 0.1 2 0 8 0.2 0 8 0.2 8/0.2 40 d q q dq q q q π = - - - = - = = = = Substituting gives: 10 0.1(40) 6 6 40 2 40 5 155 p π = - = = - - = 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 π = - = - - - - Maximizing: (100 10 ) 10 2( 10) 0 120 20 0 120 20 6 : 100 10(6) 40 6(40) 2(40) 5 155 d p p dp p p p Substituting q π π = - - - - = - = = = = - = = - - = Suppose instead Revenue is maximized. Using the inverse demand: (10 0.1 ) 0.1 0 10 0.2 0 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 π = - - = - = = = = = - = = = > = = - - = <
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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) ) 0 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 π π π π - - - - - - - - - - - - - - = - - = - - = - - = - - + = = - = - = 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 π - = = - - 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. 1000(1 0.1 ) 1000(1 0.1 )( 2) 1000[(1 0.1 ) .1( 2)] 0 1 0.1 .01 .2 0 1.2 .2 6 1000(1 0.1(6)) 400 400(6 2) 1600 q p p p F d p p dp p p p p q F F π π π = - = - - - = - - - = - - + = = = = - = = - - = - Example 4: Demand for Infrequently Purchased Goods with a Capacity Constrain
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