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SC ECON 221 - Optimization

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ECON 221 Lecture 3 Outline of Last Lecture I. What is economics?A. The study of decision makingB. Microeconomics is the study of the tiny parts that make up the economyII. OptimizationIII. EquilibriumIV. EmpiricismOutline of Current Lecture I. OptimizationII. Cost and Benefits III. Marginal analysisCurrent LectureLecture 3 (August 28) – Optimization  Optimization – People do the best they can for themselves o But almost nothing is “free”, so there are almost always costs involved  So “Doing the best that you can” does not mean “Have the most of everything”  It mean “Find the BEST balance of BENEFITS and COSTS” o In economics we are interested in direct financial costs and “opportunity costs”o Opportunity cost – The cost of an alternative that must be forgone in order to pursue a certain action. – The benefits you could have received by taking an alternative action.  Examples: - Costs associated with owning and running a coffee shop?- Costs of going to college?- Costs of volunteering at a homeless shelter? When making an “optimal” decision, you must weigh benefits and costsThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.o Weighing benefits and costs Optimization involves finding the highest “net benefit” (benefit – cost) - Ex. You run a theater and want to advertise a show you are putting on. Ads cost $100 but run once a day.o With an ad, people will learn about the show and buy tickets.o With a bunch of ads, the same people are seeing the same ad repeatedly. o You can predict how much you’ll make based on the number of ads you put up. (Ticket sales).Ads Ticket Sales Ad Cost Net Benefit0 $50 $0 $501 $300 $100 $2002 $500 $200 $3003 $550 $300 $2504 $575 $400 $175 This what the book calls “Optimization in levels”  the best choice is whichever has the highest “net benefit” o Easy because we were able to compare monetary benefits to monetary costso Ex. What if we’re thinking about how much of something to buy – for instance donuts.  Want to balance benefits from donuts, with costs Costs are just the price How do we measure benefit?o Measuring benefits: Maximum willingness to pay  If you’d be willing to pay $4 for a donut - that tells us that you’d be willing to give up whatever else you’d be able to get for $4. Number of donuts Benefit (maxwillingness to pay)Cost (Price = $1) Net Benefit1 $4 $1 32 $7 $2 53 $9 $3 64 $10 $4 65 $10 $5 5 What we’ve seen so far is “optimization in levels” o The approach that we’ll usually use is “optimization in differences” also called “marginal analysis” – both will lead to the same result  Optimization in differences/ marginal analysiso We don’t have to assess net benefit for all possible options o Instead, constantly consider benefits and costs of doing ONE MORE of something  Marginal benefit (MB) – additional benefit resulting from one more of something  Marginal cost (MC) – additional cost resulting from one more of something o Marginal – anytime you see the word “marginal” (in this class), what we mean is ONE MORE OF SOMETHING Donuts ExampleNumber ofdonutsBenefit(Max WTP)Cost (price = $1)NetbenefitMB MC1 $4 $1 $32 $7 $2 $5 1  2 $3 $13 $9 $3 $6 2  3 $2 $14 $10 $4 $6 3  4 $1 $15 $10 $5 $6 4  5 $0 $1 If MB > MC  more benefit from doing one more than cost… so you should do/consumemore If MB < MC  more cost from one more than benefit… so you should do/consume less o Do more when MB > MCo Do less when MB < MCo You’ll be best off when MB = MC, or last point where MB > MC Suppose the price of donuts increases to $1.50 Numberof donutsBenefit(Max WTP)Cost (price = $1.50)Net Benefit MB MC1 6 $1.50 $4.52 10 $3 $7 1  2 $4 $1.53 13 $4.50 $8.5 2  3 $3 $1.54 15 $6 $9 3  4 $2 $1.55 16 $7.5 $8.5 4  5 $1 $1.5 Preview of the Law of Demand – When price went up, the quantity demand went down  Optimization – means choosing the best thing o Because everything has a cost, that means finding the best option accounting for cost (or finding the highest “net benefit” option)o Do this by finding the point where MB = MC (or the last point where MB > MC) o Costs – includes direct financial costs and “opportunity costs”o Benefits – When talking about buying things, we use “maximum willingness to pay” (WTP) as our measure of “benefit” … allows for direct comparison to cost Ex. Suppose the benefit and cost to society of various levels of pollution are… PollutionReductionTotal Benefit Total Cost Net Benefit MarginalBenefitMarginalCost0 0 0 0 -- --1 20 9 11 20 92 38 20 18 18 113 54 33 21 16 134 68 48 20 14 155 80 65 15 12 176 90 85 5 10 20 Everything has a cost (when accounting for “opportunity costs”) Optimal  MB =


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