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Solved: In Exercises 91102, use an inverse matrix to solve (if possible) the system of

College Algebra | 9th Edition | ISBN: 9781133963028 | Authors: Ron Larson ISBN: 9781133963028 204

Solution for problem 93 Chapter 7

College Algebra | 9th Edition

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College Algebra | 9th Edition | ISBN: 9781133963028 | Authors: Ron Larson

College Algebra | 9th Edition

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Problem 93

In Exercises 91102, use an inverse matrix to solve (if possible) the system of linear equations. 3x 10y 5x 17y 813

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Study Guide Micro Econ Test 2 Notes Demand -If you demand something then you both want it and you can afford it. -The amount of a good that would be bought at each possible price, during some time period, given the environment. -Given the environment = everything else held constant = ceteris paribus Quantity demanded -The amount of a good that would be bought at a given price, during some time period and given the environment. -One price and one quantity. -Ex: If a Big Mac is $.99, I will buy 2. If it’s $.50, I will buy 3. If it’s $2.00, I will buy 1. Demand Schedule -A table that shows the relationship between the price of a good and the quantity demanded. Law of Demand -As price goes up, quantity demanded goes down -Other things being equal, the quantity demanded is negatively related to the price of a good. How do you find the slope of a demand curve -Price on the y-axis, quantity on the x-axis. -Will always be a downward sloping curve because they are negatively related. Individual Demand vs. Market Demand -The quantity in the market is the sum of the quantities demanded by all buyers at each price. Determinants of Demand 1. Price of the good 2. Price related to goods 3. Income 4. Population 5. Taste (preference) 6. Expectations A change in price  A change in others  A change in demand Δ (delta) = change Shift of Demand -A change in demand = shifting the demand curve. -When demand increases, the demand curve shifts to the right. -When demand decreases, the demand curve shifts to the left. -When quantity demanded changes, there is NO SHIFT. The point moves along the demand curve. Substitutes -A good you can use in replace of another. (Margarine instead of butter, Pepsi instead of Coke) -Price increases  Demand increases (a rise in the price of laptops will raise the quantity demanded of desktops) Compliment -Goods that are used together (milk and cereal, hamburger and bun) -Price increases  Demand decreases (a raise in the price of hot dogs will lower the demand of buns) Income -Normal good -A good for which an increase in income leads to an increase in demand (cars, 5 star restaurants) -Inferior good -A good for which an increase in income leads to a decrease in demand. (fast food restaurants) Population -With more people, demand increases. Taste (Preference) -If you like something more, the demand for that good increases (the new iPhone, the new Star Wars movie) Expectations -Future price changes (if you expect the price to go up in the future, you will demand more today) Supply -The amount of a good that a firm could and would sell at all possible prices, given the environment. Q: What determines how much is supplied to the market -Free markets determine how much is supplied. -The price! (Important for supply and demand) Supply Schedule -A table that shows the relationship between the price of a good and the quantity supplied. Law of Supply -As the price goes up, quantity supplied goes up -Opposite of the law of demand. -So it is positively related -As a seller, you want to make as much profit as possible. Q: What is the slope of the Supply Curve -The curve will have a positive slope and increase. Market Supply vs. Individual Supply -The quantity supplied in the market is the sum of the quantities supplied by all sellers at each price. -Just add to get the total quantity supplied! -They are also positively related. Determinants of Supply: 1. Price of the good 2. Prices of Inputs 3. Technology 4. Number of Suppliers 5. Expectations of future prices Price decreases  Quantity supplied decreases -Just like demand you MOVE ALONG THE SUPPLY CURVE Q: What is the ultimate goal in doing business -To make a profit! -Profit = total revenue-total cost -Price x quantity A change in supply -Opposite of a change in demand An increase in supply =The entire SC shifts to the right (out) A decrease in supply =The entire SC shifts left (in) Q: What determines cost of production -if a firm can produce the good cheaper then it will want to produce more of the good at all possible prices. Input prices -The cost of production. -What is used in order to create the output! -Wages cost of machines, rent, raw materials, and workers. Ex: Illegal immigrants are willing to work for low wages. This means less cost of production and the supply will increase. The supply curve will shift to the right because we are supplying more! Technology -Better technology makes firm more efficient = more output for some amount of input. Q: What other factors that effect supply Number of suppliers -If there are more firms in a industry, then more will be supplied at any price Expectation -Future prices -If you are a seller, you expect the price will go up in the future. Do you sell now or later You sell later! You will make maximize your profit! -Opposite of demand expectations Ex: Suppose there is an increase in the price of steel. We would expect the supply curve for steel beams to____ -Shift to the left -Price of inputs goes up -Cost of production goes up -Supply goes down -Therefore shifts to the left Equilibrium Price -Where price has reached the level where quantity supplied equals quantity demanded. -On the chart, the demand line and the supply line cross at this point. -A perfect market! Disequilibrium -Shortage (=excess demand) Qs < Qd -Surplus (=excess supply) Qs > Qd Three Steps to Analyze Changes in Equilibrium 1. Decide whether event shifts supply curve, or the demand curve, or both, 2. Decide in which direction curve shifts (left or right) 3. Use supply-demand diagram to see how the shift changes price and quantity. What happens when both supply and demand shifts at the same time -Supply increases, Demand increases  Price , Quantity rises -Supply decreases, Demand deceases  Price , Quantity falls -Supply increases, Demand decreases  Price falls, Quantity -Supply decreases, Demand increases  Price rises, Quantity Chapter 5 Elasticity and its Applications Elasticity -A numerical measure of responsiveness of quantity demanded or quantity supplied to on of the determinants. -Always has to do with the responsiveness between 2 variables. Price Elasticity of Demand - Measures how much quantity demanded responds to a change in price. - The size of this number determines customers’ sensitivity towards price. - Smaller numbers means people will not react as much to price changes. - Larger numbers means people will react more to price changes. Price elasticity demanded = % change in quantity demanded / % change in price Ex: -Price rises by 10%. -Quantity falls by 15%. - -15%/10% = (WILL ALWAYS BE A NEGATIVE NUMBER) the absolute value of -1.5 = 1.5 Ex: -Price falls by 10%. -Income increases by 5%. -Quantity increases by 20%. -Price elasticity cannot by calculated because there is a changing income variable. Calculating Percentage Changes Standard method (do not use because gives different answers depending on which variable you start with) -End value – start value / start value x 100 Midpoint Method -End value – start value / midpoint x 100 -The midpoint is the number halfway between the start and the end values, the average of those values. -Does not matter where you start or where you end! Change in quantity demanded / quantity average (midpoint) = (Q2 – Q1) / ((Q2 + Q1) /2) x100 Change in price / price average (midpoint) = (P2-P1) / ((P2 + P1) / 2) x100 Q: -When the price of a good is $5, the quantity demanded is 100 units per month; when the price is $7, the quantity demanded is 80 units per month. Using the midpoint formula, the price elasticity of demand is about… A: -Elasticity demanded = % change in quantity / % change in price -(100 – 80 / 90) / (7 – 5 / 6) = 22.2 / 33.3 = 0.67 The Variety of Demand Curves -The flatter the curve, the more elastic it is! -The price of elasticity of demand is closely related to the slope of the demand curve Demand Elasticity Elastic Demand Ed > 1 Unit elastic demand Ed = 1 Inelastic demand Ed < 1 Perfectly elastic demand (ex: $1 for 4 quarters) Ed = infinite Perfectly inelastic demand (ex: medicine, medical treatment) Ed = 0 Determinants of Price Elasticity 1. Availability of close substitutes (more substitutes > less substitutes) -Ex: breakfast cereal vs. sunscreen -Price goes up  which good is more elastic (Which good does quantity demanded drop) -Breakfast cereal has many close substitutes, so buyers can easily switch if the price rises. It is more elastic and people respond more to price change. -Sunscreen does not have close substitutes, and therefore is inelastic and people respond less towards price changes. 2. Necessities vs. luxuries (necessities < luxuries) -Ex: insulin vs. Caribbean cruises -Price goes up  which is more elastic -Insulin is a necessity. A rise in its price would cause little or no decrease in demand. It is inelastic and people react less to price change. -Caribbean Cruises are a luxury and you don’t really need it to survive. If it goes up you are likely not to go. It is elastic and people react to price change. 3. Definition of the market (narrower good > broader good) -Ex: blue jeans vs. clothing -Price goes up  which is elastic -For a narrowly defined good, such as blue jeans, there are many substitutes. This is elastic and people react more to price change. -For a broader good such as clothing, there are not many substitutes (nude). This is inelastic and people react less to price. 4. Time horizon (long time > short time) -Ex: Gasoline in the short run vs. gasoline in the long run -Price goes up  which is more elastic -There’s not many people that can do a short run, other than ride the bus or carpool. Fewer substitutes. People react less to price because they don’t have enough time to do so and therefore it is inelastic. In a long run, people can buy smaller cars or live closer to where they work. They have more substitutes. The long run person react more to price change and is elastic. 5. Cost relative to income (expensive good > cheap goods) -Ex: pencil vs. vacation trip -Price goes up  which is more elastic -Pencils are a small portion of a persons’ income and people don’t care. It is inelastic and people react less to price change. -Vacation trips are a large portion of an income. People react to price change and it is elastic. Price Elasticity of Demand and Total Revenue Total Revenue -Total Revenue = Price * Quantity -A price increase has two effects on revenue Price Effect -Higher price means more revenue on each unit you sell. Quantity Effect -The price increases, you make more revenue, but you sell fewer units due to the Law of Demand. Q: Which of these effects is bigger A: It depends on the price elasticity of demand. -If demand is elastic, than elasticity of demand > 1 -This means the total revenue falls. (Quantity Effect > Price Effect) -If demand is inelastic, than elasticity of demand < 1 -This means that the total revenue will rise. (Price Effect > Quantity Effect) Cross-Price Elasticity of Demand -Measures the response of demand for one good to changes in the price of another. =% change in quantity for good X / % change in price for good Y -For substitutes, cross-price elasticity >0 Ex: An increase in the price of beef causes an increase in demand for chicken. -For compliments, cross-price elasticity < 0 (negative) Ex: an increase in the price of computers causes a decrease in the demand for software. Price Elasticity of Supply -Measures how much quantity supplied responds to a change in price. =% change in quantity supplied / % change in price -It measures sellers’ price-sensitivity -In a graph, the steeper the curve, the more elastic the supply Chapter 7 Consumers, Producers Efficiency -How society can best allocate its scarce resources Allocation of resources refers to: -How much of each good is produced -Which producers produce it -Which consumers consume it Welfare Economics -Studies how the allocation of resources affects economic well- being. Marginal benefit -Measures how much a buyer values a good -The benefit a person receives from consuming one more unit of a good. -The max amount that a person is willing to pay for an additional unit of a good. -The willingness to pay Ex: -You’re willing to pay $5 for one slice of pizza because you are super hungry. -You’re still hungry, but not as much, so you’re willing to pay $3 for the second slice. -For the third slice, you’re even less full and less desperate for food, my willingness to pay is $1 The principle of decreasing marginal benefit -MB decreases as you consume more of a good. -Demand Curve = Willingness to Pay Curve = Marginal Benefit Curve -The demand curve looks like a staircase. (one step per buyer) Consumer Surplus -The amount a buyer is willing to pay minus the amount the buyer actually pays. -Consumer Surplus = Willingness to Pay – Price = Marginal benefit – Price Consumer Surplus = the area under the Demand and above the Price. Ex: -Price is $260 -Ryan’s willingness to buy is $300 -300 – 260 = 40 -Consumer Surplus = $40 Q: Your sister inherits a doll from your Great Aunt. The doll has a sentimental value of $500 to you. Your sister sells the doll to you for $200. What is your marginal benefit A: 500-200 = $300 Q: Sam is willing to pay $10 for one bracelet and $5 for a secone. Isabella is willing to pay $12 for one bracelet and $2 for a second. If the price of the bracelets are $8, what is the total consumer surplus after they make their purchase A: Sam’s willingness to pay = 10 - 8 = 2 Isabella’s willingness to pay = 12 - 8 = 4 $4 + $2 = $6 Marginal Cost -The O.C of producing one more unit of a good or service. -The curve on a graph is an upward sloping staircase. Producer Surplus = Price – Marginal Cost -Total Producer Surplus equals the area under the price and above the surplus. Total Surplus CS = MB – P =Buyers’ gain from participating in the market PS = P- MC =Sellers’ gain from participating in the market Total Surplus = CS + PS =Total gains from trade in a market =(Value to buyers) - (cost to sellers) = MB – P + P – MC = MB – MC Efficiency -Total surplus -An allocation of resources is efficient if it maximizes total surplus -On a graph this means the whole area is filled. -Raising or lowering the quantity of a good would not increase total surplus -NO DEADWEIGHT LOSS Produce at Marginal Benefit = Marginal Cost (Equilibrium) Deadweights loss -The loss in consumer surplus or producer surplus that results from an inefficient level of production. -On a graph, there would be vacant areas and would not be space would be incomplete. -Underproduction: Marginal Benefit > Marginal Cost -Overproduction: Marginal Benefit < Marginal Cost Ex:  Price ceiling and floors  Taxes, subsidies, and tariffs  Externalities  Public goods  Monopoly Study Guide Micro Econ Test 2 Q/A’s Q: Price elasticity of supply is: a) positive in the short run but negative in the long run. b) Independent of time c) Greater in the short run than in the long run d) Greater in the long run than in the short run Q: If the supply of product X is perfectly elastic, an increase in the demand for it will increase: a) equilibrium quantity but equilibrium price will be unchanged b) equilibrium price but reduces equilibrium quantity c) equilibrium price but equilibrium quantity will be unchanged d) equilibrium quantity but reduces equilibrium price. Q: If price of product X increases, the demand curve for close- substitutes product Y will: a) remain unchanged b) shift downward toward the horizontal axis c) shift to the right d) shift to the left Q: Suppose an economist says “Other things equal, the lower the price of bananas, the greater the amount of bananas purchased.” This statement indicates: a) one cannot generalize about the relationship between the price of bananas and the quantity purchased b) the quantity of bananas purchased determines the price of bananas c) all factors other than the price of bananas are assumed to be constant d) economists can conduct controlled laboratory experiments Q: The more time consumers have to adjust to a change in price: a) the more likely the product is a normal good b) the greater will be the price elasticity of demand c) the more likely the product is an inferior good d) the smaller will be the price elasticity of demand Q: Which of the following is assumed in constructing a production possibility curve a) resources are perfectly shiftable among alternative uses b) the economy is using its resources inefficiently c) the economy is engaging in international trade d) production technology is fixed Q: Economist use the term “demand” to refer to: a) the total spent on a particular commodity over a stipulated time period b) an upsloping line on a graph that relates consumer purchases and product price c) a schedule of various combinations of market prices and amounts demanded d) a particular price-quantity combination on a stable demand curve Q: Suppose that as the price of Y falls from $2 to $1.90, the quantity of Y demanded increases from 110 to 118. Then the price elasticity of demand is: a) 1.37 b) 4.00 c) 2.09 d) 3.94 A: A A B C B D C A

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Chapter 7, Problem 93 is Solved
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Textbook: College Algebra
Edition: 9
Author: Ron Larson
ISBN: 9781133963028

This textbook survival guide was created for the textbook: College Algebra, edition: 9. This full solution covers the following key subjects: . This expansive textbook survival guide covers 9 chapters, and 5750 solutions. The full step-by-step solution to problem: 93 from chapter: 7 was answered by , our top Math solution expert on 01/02/18, 09:21PM. The answer to “In Exercises 91102, use an inverse matrix to solve (if possible) the system of linear equations. 3x 10y 5x 17y 813” is broken down into a number of easy to follow steps, and 21 words. Since the solution to 93 from 7 chapter was answered, more than 249 students have viewed the full step-by-step answer. College Algebra was written by and is associated to the ISBN: 9781133963028.

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Solved: In Exercises 91102, use an inverse matrix to solve (if possible) the system of