This Weeks TopicsReview Class ConceptsAC/MC Rules of OverheadSimple PricingPrice Elasticity of DemandReview HomeworkPractice Problems
Class Concepts AC/MC Rules of OverheadSequential DecisionsShould I produce the first product? Is the price I can sell at greater than average cost? Should I, also, produce the second product? Is the price I can sell at greater than marginal cost? Knowledge Check: Which orders would I accept, if I received the following sequentially (not knowing I would receive the subsequent orders)? FC = 200, MC = 5Order 1: 100 units, Price = $6.50/unitOrder 2: 200 units, Price = $6.01/unitOrder 3: 50 units, Price = $5.50/unit
Class Concepts AC/MC Rules of OverheadSimultaneous DecisionsYou receive two orders at the same timeShould I produce the first product or the second product or both or neither? If the price for a product is less than MC, do not produce itProduce only one product if:The price for the other product is less than MC andThe price of the product is greater than the ACProduce both products if: The total revenue of both products exceeds the total cost: Total Revenue Total Cost P1*Q1 + P2*Q2 FC + MC*(Q1 + Q2)
Class Concepts AC/MC Rules of OverheadKnowledge Check: Should I produce Product 1, Product 2, both or neither? FC = 200, MC = 5Fixed costs are shared by both products. Marginal costs are the same for both productsA) Product 1: Q = 100, P = 6 Product 2: Q = 50, P = 10B) Product 1: Q = 100, P = 4 Product 2: Q = 200, P = 6
Class Concepts Optimal Simple PricingSteps for Solving an Optimal Simple Pricing Problem1) Identify your total cost function (TC) and inverse demand functionFind the inverse demand function by finding the demand function and solving for P2) Solve for marginal cost (MC) and marginal revenue (MR) by taking derivatives3) Set MC = MR, and solve for Q*4) Insert Q* into your inverse demand function and solve for P*5) Check that you are profitable: Profit = Total Revenue Total Cost = P* x Q* TC 0** Be sure to do the last step! Optimal Simple Pricing helps you figure out the most profit you can make from selling a good, given available demand. Is that optimal profit high enough to cover your fixed costs?
Class Concepts Optimal Simple PricingKnowledge Check You are considering selling a new productTo produce the product you will need to buy a machine for $500, and each unit will require $10 is materials and $2 in labor and $3 in shipping costs to produce. You have already purchased market research (which is 100% accurate), that tells you that you can expect the following purchasing patterns by customers:
Should you sell the new product? If so, what is the optimal price you can sell your product at?
Class Concepts Optimal Simple PricingSolutionStep 1: Find demand and cost functionsCost = 500 + 15QDemandPlot in Excel and find a best-fit line ORSlope = (y2-y1)/(x2-x1) = (150-100)/(20-40) = 50/-20 = -2.5P = slope x Q + intercept 150 = -2.5 x 20 + intercept intercept = 200P = -2.5Q + 200Step 2: Find MR and MCRevenue = P x Q = (-2.5Q + 200) x Q = -2.5Q2 + 200QMR = derivative of (-2.5Q2 + 200Q) = 2*-2.5Q + 200 = -5Q + 200MC = derivative of (500 + 15Q) = 0 + 15 = 15
Class Concepts Optimal Simple PricingSolutionStep 3: Set MR = MC and solve for Q*-5Q* + 200 = 155Q* = 185Q* = 37Step 4: Insert Q* into the inverse demand function and Solve for P*P* = -2.5Q* + 200 P* = -2.5(37) + 200P* = -92.5 + 200 P* = $107.50
Class Concepts Optimal Simple PricingSolutionStep 5: Is the solution profitable? P* = $107.50, Q* = 37Profit = P* x Q* - Total Cost = P* x Q* - FC - MC x Q*Profit = (107.50)(37) (500 + 15*37)Profit = $3977.50 $500 $555 = $3977.50 - $1055Profit = $2922.50So, you should produce the product, and the optimal price you can sell your product at is $107.50
Class Concepts Price Elasticity of DemandPrice Elasticity of Demand
Class Concepts Price Elasticity of DemandDefinition
General Definition Exact DefinitionUse the general definition to solve for the elasticity between two sets of known prices and quantitiesUse the exact definition to solve for the elasticity at a specific point. You need the demand function and the price.
Class Concepts Price Elasticity of DemandElasticity Types|| > 1Elastic (if price goes up, revenue goes down)|| < 1Inelastic (if price goes up, revenue goes up)|| = 1Unit Elastic (if price goes up, revenue does not change)Elasticity and Revenue Relationship
% Change in Revenue = % Change in Price (1 + )
Class Concepts Price Elasticity of DemandLerners Mark-up RuleIf you know the demand function, you can use simple pricing to solve for the optimal price. However, if you only know demand at two prices, or you only know the price elasticity of demand, then the Lerner Mark-up Rule can help you solve for a more optimal price
Note: You can only use the Lerner Mark-up Rule when demand is elastic || > 1. If demand is inelastic, you can continue to raise your price, and your revenue will increase. You can only use the results of the Lerner Mark-Up Rule if the resulting optimal price is close to your original known demand points
Class Concepts Price Elasticity of DemandKnowledge Check1) If price increases by 3% and elasticity is -1.9, how will revenue change? 2) You know the following demandQ1 = 200, P1 = 50Q2 = 190, P2 = 52Interpret the elasticity of demand in words.What is the optimal price if marginal cost is 45? 3) If demand is Q = 80 0.4P and price is 20What is the elasticity of demand at the current price? What does this tell us about the current price?
Class Concepts Price Elasticity of DemandKnowledge CheckQuestion 1) dR/R = 3%(1+(-1.9)) = -2.7% Revenues will decline by 2.7%Question 2) = [(200-190)/195]/[(50-52)/51] = 0.513/-0.039 = -1.308The demand is elastic. If you increase the price, revenues will decline. Lerners Mark-up Rule: P = 45/[1+(1/-1.308)] = 191Question 3)Use: Derivative of (80 0.4P) = -0.4Q = 80 0.4*20 = 72 = -0.4/(72/20) = -0.4/3.6 = -0.111
Homework Review Question 1Widget-Making FirmOpportunity Costs = $50,000 x 12 months = $600,000First-Year ExpendituresLoan Interest = $4,000,000* 6% = $240,000Equipment Maintenance = $80,000Materials + Labor + Utilities= $2,080,000Total Expenditures = $2,400,000$4,000,000 spent on machines is not an expenditure because the machines are maintained and can be resold for $4,000,000Increase in Revenue must be at least $600,000 + $2,400,000 = $3,000,000
Homework Review Question 2Earthquake InsuranceThe likelihood of both quakes occurring simultaneously is very low. Buy low levels of insurance on the occurrence of both quakes. If one of the quakes occurs, immediately use the payout from that insurance to buy additional insurance for the second quake. Let I be the amount of insurance purchased for each quakeIf the Japanese Quake occurs, the insurance pays out 5I. Buy California insurance.You now have 6I California Quake insuranceThe insurance will pay out 5*6I, or 30I if the California Quake hits. 30I = $10,000,000I = 333,333.34So, the company should buy $333,333.34 in insurance on the Japanese Quake and buy $333,333.34 in insurance on the California Quake
Practice QuestionsQuestion 1 (Ch. 8, Q5 in Samuelson & Marks)A firm faces uncertain revenues and uncertain costs. Its revenues may be $120,000, $160,000, or $175,000 with probabilities 0.2, 0.3, and 0.5, respectively. Its costs are $150,000 or $170,000 with chances 0.6 and 0.4, respectively. What is the expected profit? How much would the firm pay for perfect information about its costs?
Practice QuestionsQuestion 2 (Ch. 8, Q3 in Samuelson & Marks)For five years, a firm has successfully marketed a package of multitaks software. Recently, sales have begun to slip because the software is incompatible with a number of popular application programs. Thus, future profits are uncertain. In the softwares present form, the firms managers envision three possible five-year forecasts: Maintaining current profits in the neighborhood of $2 million, aslip in profits to $0.5 million, or the onset of losses to the tune of -$1 million. The respective probabilities of these outcomes are .2, .5, and .3An alternative strategy is to develop an open or compatible version of the software. This will allow the firm to maintain its market position, but the effort will be costly. Depending on how costly, the firm envisions four possible profit outcomes: $1.5 million, $1.1 million, $0.8 million, and $0.6 million, with each outcome considered equally likely. Which course of action produces greater expected profit?
Practice QuestionsQuestion 3 (Ch. 2, Q6 in Samuelson & Marks)A television station is considering the sale of promotional videos. It can have the videos produced by one of two suppliers. Supplier A will charge the station a setup fee of $1,200 plus $2 for each cassette; supplier B has no setup fee and will charge $4 per cassette. The station estimates its demand for the cassettes will be given by Q = 1,600 200P, where P is the price in dollars and Q is the number of cassettes. If the station plans to give away the cassettes, how many cassettes should it order? From which supplier? Suppose the station seeks to maximize its profits from sales of the cassettes. What price should it charge? How many cassettes should it order from which supplier?
Practice QuestionsQuestion 4 (Ch. 2, Q12 in Samuelson & Marks)As the exclusive carrier on a local air route, a regional airline must determine the number of flights it will provide per week and the fare it will charge. Taking into account operatin