Unit 1 Review PDF

 & · ·  Self-responsibility I like constructive criticism My preferences Office hours are a great resource There’s no free lunch  Three sections Consumer Firms Markets Our program...

 & · ·  Self-responsibility I like constructive criticism My preferences Office hours are a great resource There’s no free lunch  Three sections Consumer Firms Markets Our program Tests (3) Homeworks (6) Who puts Micro in microeconomics? What or who will be the subject of our work this semester? What’s the smallest economic agent? What are THE economic roles? People, People, People Consumers: I want, you want, we want… NOW! Firms: Money! Money! Money! Markets: More! Less! More! Less! THE economic problem Why do we have a market for gold –which no one needs– but do not have a market for air –which everyone needs–? Predict: will there be a market for sand in the Sahara? What’s (not) missing?? Fixing Scarcity Consider bread. How to make it abundant (as opposed to scarce)? 1. Make more than is wanted - Would you buy more bread than you wanna eat? - Would you bake bread just to go to waste? How to coordinate? The Market’s signal How can the market achieve the coordination of consumers and firms? How do I know if I want one or two loafs for breakfast? How do I know if I should increase or reduce my bread production? Economics 101 What’s missing from this picture: 1. A baker can produce 10 loafs of bread an hour 2. Each loaf costs $3 to produce 3. Each loaf can sell for $8 Economics is Simple People = rationality + more is better than less What about my age, sex, profession, hobbies? The two economics - It is big, grey, has a trunk, big ears, and ivory tusks - It is scary, and it will trample you or grab you with its trunk and throw you against a wall Positive Economics Descriptive Agreement based You’d expect it would be easy to agree that elephants are gray… Normative Economics What Should be done or Should take place Results in Norms or Laws (or is the result of) No agreement necessary Chp 1 : - changes in Qd : consumer taste , information/advertising , prices of other goods , incomes , government rules and regulation demanded quantity in - price creates a change  1. Demand Demand a. What’s my demand for X? a. How much do I want? and b. What’s the demand for X? a. How much is wanted? Supply 101 c. Conditional on? a. What do we take for granted? Demand for Coffee What matters most if you want to buy coffee: a) Attractive bartender b) Weather in Brazil c) Price d) neither e) other, say out loud The Demand function What’s this? 𝑄𝑐𝐷 = 𝑓(𝑝𝑐 ) Lets add some information: - Say that we here would take 100 coffee cups if they were given out free - Say that none of us is willing to pay $10 for a cup of coffee. Can we graph this information? j mana o it -a so Fill in the Demand function What’s the relationship between Quantity and Price? Do I want more or less when price goes up? The Law of Demand > - DMPN price ↑ want less 𝑄𝑐𝐷 = 𝑎 ± 𝑏 ∗ 𝑝𝑐 Q = a - b · P How to determine a? I & slope : how sensitive Can we make Q=a? Intercept Qd is to The a= max quantity demanded 1Qd when p = o) changes in price to determine think abt when , its free How to determine b? What is the relationship between Q and b? -b shows price elasticity demand - if small price results large big is b , a change in in a change in demand Determining the Demand Function 1. Locate two points in cartesian plane and connect them with a straight line 2. Find value of intercept (a, What is the demand when p=0?) 3. Find value for slope (b, How much does quantity change when price is $1 higher?) Example: The city of Austin could consume 30 tons of chocolate if it were handed out for free. However, no one in the city would eat chocolate if the price were to reach $5 million per ton. Some Rules 1. X and Y need labels (Q, P) 2. Axis have direction 3. Any point should be labeled somehow 4. The Economist way: assume away, make it simple! Dynamics - Demand A change is observed in the quantity demanded; it must have happened that… when price of the good swifts ~ a) We moved along the current demand curve b) We moved the demand itself - factors other than price changes - consumer pref , income , subs/comp Consider a), what would cause a change in quantity demanded? 𝑄𝑐𝐷 = 100 − 10𝑝𝑐 PRICE would change and &  that determinants - factors influence the demand for Displacing the demand goods/services beyond just price What may we call demand “Determinants”? Why would we want to drink coffee, eat bread, have a yatch? 1. Preferences > - trends , cultural influences , advertising due to lifestyle changes societal norms ~ often change marketing , , and evolving 2. Environmental factors > - recessions , growth, inflation , interest rates , employment , , government expectations about the future Preferences - Tastes: you prefer coffee over tea, or soda over coffee - Information: Taylor Swift loves coffee coffee is good/bad for your blood pressure How to evaluate the effect of these factors on the demand for coffee? How can we enter them into the demand function? Modifying the Demand function 𝑄𝑐𝐷 = 100 − 10𝑝𝑐 How can we modify this function so that 𝑄𝑐𝐷 = f(𝑝𝑐 ,X)? Why is X not in the demand function to begin with? What happens if we consider X to be a constant? Environmental Factors 1. Expand the demand for coffee to be a function of the price of tea: Is their relationship positive or negative? Are they complements or substitutes? substitutes ; Prea & Profe * and rice versa 2. Suppose the price of tea goes down. Ceteris paribus, what does the new demand function say? Prea ↓ Drotte + 3. Draw a new demand for coffee Closer or farther from the origin? Is the demand higher or lower overall? Original DC "I -Dc after P- ↓ Other factors (Environmental) Wealth Types of goods State Regulation Taxes and subsidies Demand Aggregation We determine this classroom demand for coffee. If we imagine there’s another group in the next classroom with the same demand… What is our combined demand for coffee? -Is there more people willing to buy coffee now at $5? just add the equations -How much coffee is demanded now at prices over $10? price price · 10 10 ? 100 Quantity 100 Quantity Q : 20 + (p)  2. Supply Demand a. What’s my demand supply for X? a. How much do I want is wanted? and b. What’s the demand supply for X? a. How much is wanted? Supply 101 c. Conditional on? a. What do we take for granted? Defining Supply What is being supplied? services goods and What is the most important information to determine supply? it How different/similar is the supplier from the consumer? - demand comes from the consumer - goals are different - run by profit ? Supply for Coffee What matters most if you want to sell coffee: a) Attractive bartenders b) Weather in Brazil c) Price d) that you like coffee e) other, say out loud Why do we demand/supply 1. We like X Demand 2. We think X is good for us Demand 3. X gives us a good profit supply The Supply function What’s this? 𝑄𝑐𝑆 = 𝑓(𝑝𝑐 ) Lets add some information: - Say that I would be willing to sell 18 coffees at $1* - I would be willing to sell 74 cups at $8 Pa ↓ Can we graph this information? $8- ⑧ supply $1 - 8 in zi a Fill in the Supply function What’s the relationship between Quantity and Price? Will I sell more or less if price goes up? The Law of Supply > - PaS4 More! 𝑄𝑐𝑆 = 𝑎 ± 𝑏 ∗ 𝑝𝑐 as How to determine a? Can we make Q=a? intercept of curve when supply a = p = 0 ~ minimum supply a producer is willing to offer How to determine b? What is the relationship between Q and b? b = price elasticity of supply responses in terms ~ slope of supply curve snows now much as changes in of price Determining the Supply Function 1. Locate two points in cartesian plane and connect them with a straight line 2. Find value for slope - 3. Find value of intercept  - Dynamics - Supply A change is observed in the quantity supplied; it must have happened that… in price - and vice versa mange &S4 a) We moved along the current supply curve b) We moved the supply itself & other factors such as production costs , technology , gou. reg or the number of suppliers change Consider a), what would cause a change in quantity supplied? 𝑄𝑐𝑆 = 10 + 8𝑝𝑐 RCE  determinants- factors that can cause changes at the same price Displacing the supply What may we call supply “Determinants”? Why would we want to sell more/less coffee at the same price? 1. Preferences? doesn't change 2. Environmental factors? - input costs technology - gou policies and regulations (tax) - supply chain /global trade - Modifying the Supply function 𝑄𝑐𝑆 = 10 + 8𝑝𝑐 How can we modify this function so that 𝑄𝑐𝑆 = f(𝑝𝑐 ,X)? What could X be? Why is X not in the supply function to begin with? What happens if we consider X to be a constant? Environmental Factors 1. Expand the supply for coffee to be a function of the cost of coffee beans: Is their relationship positive or negative? Why? negative , if it costs less , producers are going to produce less 2. Suppose the price of the beans goes up. Ceteris paribus, what does the new supply function say? 3. Draw a new supply for coffee Closer or farther from the origin? Is the supply higher or lower overall? Supply Aggregation Let’s take the example from the book (Perloff 5th ed). What is Japan’s total rice supply? need to horizontally · sum Ototal · = Qj + Qi Japan Imported price price p* 𝑝 p* 𝑝 ? 𝑄𝑗 Quantity 𝑄𝑖 Quantity results in total supply curve positioned further to the right Regulation and Supply What happens to this supply if the government forbids importation of rice? imports don't affect the domestic therefore Japan's production is the only producer so pt Japan Imported price price p* 𝑝 p* 𝑝 ? 𝑄𝑗 Quantity 𝑄𝑖 Quantity Market Equilibrium 101  How do we find the equilibrium? Equilibrium between what? Consumers? Firms? Demand? Supply? Scarcity? What does equilibrium mean? What values do we expect at equilibrium? market equilibrium * Qd = Qs Moving to Market How do we integrate the parts? Demand for Coffee Supply for Coffee price price 10 8 1 ? 100 Quantity 100 Quantity  10 100-10pa : + opc lot The Market for Coffee To - price 𝑄𝑐𝐷 = 100 − 10𝑝𝑐 𝑄𝑐𝑆 = 10 + 8𝑝𝑐 10 S excess u supply Where’s the Equilibrium? p*+1 ------- + p* · (50 , 5) pt = 5 , a = so p* -1 - - -rain- Where do we have “excess” demand? excess demand - excess demand is when p is below equilibrium price 1 of 18 units D Q* 100 Quantity Example Excess Where do we have “excess” supply? Q* = 100 - 10(4) = 60 a = 10 + 0(4) = 42 Comparative Statics – Shocks! Book example. Coffee price can be affected by cocoa price. Why? Any farmers taking this class? What happens to the graph below if cocoa price goes up? price if cocod prices increases , farmers are going to produce Si want more that be they S. I would swift to left 10 profit & p* · new eq. 1 D Q* 100 Quantity Comparative Statics – Algebra…! How will an environmental change for the supply (in for example factor a) impact the coffee market equilibrium? By definition “a” displaces the supply for coffee, therefore 𝑝𝑐 = 𝑓 𝑎 Shapes are important The Demand for coffee can be different, for example? What if there’s no other source for water other than coffee? demand for coffee would be inelastic What if tea was considered nearly the same thing as coffee? demand for coffee would be elastic Elasticities elastic demand I > %Δ𝑧 Δ𝑧/𝑧 𝛿𝑧 𝑥 change in price = = ∗ %Δ𝑥 Δ𝑥/𝑥 𝛿𝑥 𝑧 - small in results in large change quantity demanded inelastic demand adjust units -change smaller change in unit elastic demand price leads in QD to = a 1 F provide e a change -change in price leads to marginal change a proportional change in in a with respect quantity to P Demand Elasticity That would be how responsive demand is to changes in…? price In our example 𝑄𝑐𝐷 = 100 − 10𝑝𝑐. How can we estimate demand elasticity? * and Q *= Q so 100 - 10(PC) 5 = if = p price elasticity of demand : : - 'slope D of curve, take derivative  Elasticity along the Demand and quantitisa higherprices lower -at - at midpoint, demand is unit elastic price - at lower prices and higher more elastic demand is inelastic 10 quantities , 𝜂 ≷ −1? 7 𝜂 = −1 un't elastic 5 3 𝜂 ≷ −1? more inelastic Quantity 30 50 70 100 Different Demands A demand may have constant Elasticity, meaning? priceelasticity of demand remains the same at all points It may be completely elastic, meaning? Why would demand disappear when the price of a good increases? small change in price - disappearance of demand - horizontal line caused by perfect substitutes It may be completely inelastic, meaning? Why would demand be unresponsive to price? An does not change - regardless of price - vertical line caused by absolute necessities Alternative Elasticities synonymous - THE demand elasticity is price elasticity, but there are other interesting relationships… 1. Income elasticity of demand, define? responsiveness changes of consumer's · Qd to of the income 2. Cross-price elasticity of demand, define? responsiveness of the Qd for one good to a change in the price of another Income elasticity of demand %Δ𝐷 Δ𝐷/𝐷 𝛿𝐷 𝑌 = = ∗ %Δ𝑌 Δ𝑌/𝑌 𝛿𝑌 𝐷 What would be the “normal” response of demand to an increase in income? normal good : it income t is positive , demand increases with income Why do we care? nothing ~ , electronics , going out inferior good : if income t is negative , demand decreases with income ~ canned goods , used goods Cross-price elasticity of demand %Δ𝐷𝑥 Δ𝐷𝑥 /𝐷𝑥 𝛿𝐷𝑥 𝑃𝑦 = = ∗ %Δ𝑃𝑦 Δ𝑃𝑦 /𝑃𝑦 𝛿𝑃𝑦 𝐷𝑥 Changes in the prices of which goods are likely to reduce (increase) coffee demand? substitutes : if cross price elasticity is positive , price of good 1 increases , demand for good 2 ↑ Why is it useful? ex : if tea price &, coffee demanda complements : if cross price elasticity is negative, price of good 1 increases , demand for good 2 ↓ ex it sugar price & demand for coffee + : , Supply Elasticity In the same way, we can get information about the supply by calculating its price elasticity %Δ𝑆 Δ𝑆/𝑆 𝛿𝑆 𝑃 = = ∗ %Δ𝑃 Δ𝑃/𝑃 𝛿𝑃 𝑆 Any difference to demand elasticity? measures now much quantity supplied change in response to price change Comparing “terms” (long/short) Responses from both consumers and producers may be different when we change the horizon What do you do if electricity is forecasted to be more expensive this September? Would you do something different if the cost never goes back down? Similarly, if you are a car producer confronted to a two-month demand surge vs. a sustained and apparently permanent demand increase, would you be more flexible in one case? Effects of taxes on Equilibrium Question 1: It is better when taxes are set on ___ a) consumers tax incidence- distribution of the tax burden b) producers between consumers and producers 8 c) either Question 2: Taxes are payed by ___ a) consumers b) producers Oc) either Other Government interventions Subsidies Opposite of taxes. Price ceilings Can charge no more than X for this good or service Price floors Must pay at least X for this good or service  In economics individuals have: Preferences The Individual Maximizing Behavior Limitations! - Logical Lexicon Does this make sense to you: coffee > tea bagel > croissant ? If a weakly prefers consumer Preferred 7 a to b (a2b) and does not weakly prefer b to a 1b a) Indifferent ~ al b then we say ↑ -> Weakly preferred ↓ consumer preferences : that bundles these relationships completeness - rules out the possibility the consumer cannot rank the ; have to be true ex : a = b b =a , a - b , D2C transitivity : if a consumer prefers a = b and , then the consumer also weakly prefers a to c , a ? of more-is-better : more a commodity is better than less of it ; consumers can dispose of excess goods so consumers can be no worse off w/ extra goods reflexive : any option or bundle is as at least as good as itself ex : 2 a From “I rather” to Inequality What should I know? You can prefer a bagel to a croissant or viceversa… can you not have a preference? Be reasonable Can you attach more than one value to one thing? Be sensible If a bagel is better than a croissant and a croissant is better than a danish, then a bagel is ____ to a danish? better ! Mapping preferences Given these conditions we can tell when bundles of two goods CAN be in the same indifference curve, and when they CANNOT. Compare bundles of (bagels,croissants): A (4,5), B (5,3), C (3,4), D (2,7), E (2,1) connecting the bundles that give the same pleasure are indifferent curves Using Indifference in preferences A set including every bundle that we consider equivalent is an “Indifference Curve” “I’d be as happy with 5 bagels and 5 croissants as with 4 bagels and X croissants.” Improving away from origin (0,0) - more is better Cannot cross each other Downward slope (> convex) Q2 A as a consumer gets more good and , less of goods , they LESS willing to trade good for good , be they value goods more highly as quantity diminishes indifference curve consists of all bundles that correspond with a specific utility measure If a utility function is u(g., 92) then the expression for the indifference curve is # determines that all those bundles = u(9 92).. < of 9 , and go give it utils  substitutes perfect same utility between two goods : :* straight lives be same utility ; you can just swap them out u(9 ,, 92) : ag , + b92 perfect complements consumed in fixed proportions T · consumer L shaped be gets no additional utility from consuming more good of one wont the > corresponding increase of the other Q, good U19 , 92) : nnlag , 192) where a and b indicate the fixed proportion in wruch goods are consumed  Functions Utility : a 1) Cobb Douglas - U19 ,, 92) = gage" # of bought music 92 = # of live music events 9. = MRS = ? U = 99921-a current ratio of -now live music many ")) mu , · : alq , events she attends vs. tracks bought / Muz = : (1-a)q , reflects relative recorded preference for music vs. live music Mrs 92 vs. Cobb Douglas 24 : 18 2) If 9 : , 92 0 6 a = 4 "az %. u. , 9 = b = 0. 6 Mrs : : = 7 = - 0. 5 Indifference Curve Extremes Perfect Substitutes # MRS = - Perfect Complements E 2. Limitations Why don’t we just eat all the bagels and croissants? Why don’t you have a gold iPhone 15/Galaxy S24? Why are you forced to dress yourself? Kings didn’t have to stoop so low… Budget Constraint croissants How will it look like? How many goods can we buy with our income? straight line ; maximum combinations of two goods that can be bought wi budget What information is contained in the slope of our budget constraint? slope represents Opportunity cost bagels slope- Optimal bundle What would this be? croissants i.e., what’s our objective when consuming? a Can you find it in the graph? Y maximize · utility subject constraint b to budget 8c Y bagels  constraint Budget : ex1) price ratio between two 3/1 and goods is good increases from ↓ ot budget of $100 price ina - a. If 6 to 12 , What is the new price ratio ? represents the bundles D that you can afford. Y budget : constraint : p. 9 , + P292 Pizza marginal rate of transformation : slope of budget line quita corre -measures opportunity cost rate at which you give - up one good for another based on income MRT = = We want all... we can get That’s just plain English for we maximize our utility subject to our budget (constraint) Mathematically, 𝑚𝑎𝑥𝑈(𝑞1 , 𝑞2 ) Subject to Y=… Finding Optimal Bundle Replacement Lagrangian Minimization? Lagrange optimal indifference bundle curve : highest that touches the budget line ; highest utility against What if we have three goods? income Or n goods for that matter, is it intelligible? Mrs Mr What if the goods are perfect substitutes? Draw the IC and the BC… do you see a problem? utilities equal marginal are theres not a unique optimal to each other bundle , theyre the same - Lagrange Maximization : n = - /x + y = - x + 4 4x 4 16 40 + 16 : $40 BC = PL - : : Income = , pX , 2 = - x + + y + x(u0 - ux - ky) S : BC 10-ux-16y utility : : 10-1(2) - 16y 3 u = - 1/2 + 2 : -i ly y = 2 constant elasticity of substitution : - u (a., 92) : 199 + an)" max 19., 92) · 19. 0 + 92)" 91 , 92 St. Y = p , 9 , + P292 4 9. = 5292 - ni , 92) : E #E g) + % [q + q) (pqp  problems : Utility maximization 1) u(x , y) = k + j : x + y : Yx increasing -- concave maximization 2) consumer DC : Y = 0 9. , + P292 y = rx + jy + x(y - pyx - pzy) * Rpyy by : * = Y pxX - x - Y (y) 0 : 0 pxx pyy - - = Y - pxX - px Ty Opposite but equivalent We can maximize our utility given our budget constraint or… Can you turn the statement around? of utility minimize expenditure to achieve a given level Can we set up a Lagrangian for this situation? Indirect utility and Expenditure function Indirect Utility If utility depends on consumption of goods, and the consumption of goods depends on your income and prices, then… indirect function utility function of · : and the consumers income prices of goods Similarly… · v(p m) , : where P is a rector prices for goods, m is a budget  indirect functions : · if a consumer with income m faces prices p , and pr , what is the maximum amount of utility they could have · utility at the optimal bundle Steps : 1) get optimizing bundle from utility function * goods * have x ana y budget const max In (cb) ② Aug in. CY. St I = PcC + PDB I = P((B) + Pa I = PoB + PoB ① Find optimal I = 2Po B u1c , b) : Inc + ind E B : Frp 2 (n(c) = + (n(b) + x)I - PcC - Pub) optimal Bo- bundles a ③ ping into util function indirect : v(pc , Pb , F) = max (U (c , bs) St , BC v(pb , pr ,) = in ) (2) Cobb Example : Douglas u(x , xz) = (x , + xz) Responses to Changes Schedule for this week We’ll consider dynamics of our demand this week (Perloff, ch4) 1. Derive our demand 2. Evaluate income changes 3. Evaluate price changes How can we find the demand? What changes and what doesn’t?? croissants 𝑝1 ? , 𝑝2 ? , 𝑌? Hint: if we move a demand determinant, 𝑞𝑐∗ then… 𝑞𝑏∗ bagels  2. Income changes Y = p9 I croissants D Let’s suppose we move income A Incomeconsumption a · Do we get the demand out of this exercise? causes shift in demand curve 𝑞𝑐∗ Engel cure Engelweed YX normal L good F · income 𝑞𝑏∗ · bagels 9, 9293Q. Q , Q as 14 Q + as 1 & , 4 , ,  and income engel curve : relationship between quantity 3. Price changes Can we stay with the Engel curve if the croissants price of bagels goes up? What IS the Engel curve? Say both prices change in equal proportion, then…? substitution effect : consumption is affected by a good's change in price subject to their income bagels consumption due income effect : change in consumers to changes in income Hicksian demand We can try and compensate the individual so that utility remains constant What formula have we seen that keeps utility constant? If we compensate for income change, what’s left? Sheperd's Lemma · minimizing expenditure func. and finding Hicksian demand E(p., P2 U) : P. 9 , + page ,  MATERIAL : In class Review demand ~ det - - equilibrium ~ : Sheperd's Dilemma const max. I min - expenditure function = compensatea demand/supply - a - demand - elasticities ~ normal , inferior goods const budget. Expenditures preferences ~ -indiff curves ~ ~ - indirect utility A : no need for comp. demand -income and sub effect P decision under - uncertainty # loss of income, for when ur comp expected utility and value. ~ can consume more you - VIE) - indirect utility -Sheperd's Lemma 9 ~ constant indirect utility E(P , Pc , 4) = vI)" - v(p , p2 , 1) : Und , *, 92 * ) · if p ↑ ↓ · , ↑ , exp. , 9 , 9  Cobb Douglas : ul u(x , y) = x dy8 Y = , p , x + p - Y set up I x(Y max y = u(x j) PxX pyy) - , + - X , y , X Ex : 0 1 : = 0 = * 0 Y - Pe = pxX - budget. const  Th Session : Test Review Sheperd's vemma : S = Marshallian Demand - dependent on income and prices ⑪ converting to expendin opt. Hicksian bundle = ) ) , t get this from I 5) * e = F (n , income needed to get this level of utility -expenditure function is now much income you need used in Marshallian Demand -Hicksian is how many goods to achieve utility u(x , xz) = (x , + 1)(x + 1) xz) Yz = u(x X , + x1 + xz + 1 , BC : I - P x - PX) = 0 , , Method indirect utility Function : MRS : : u(x xz) (x 1)(xz + 1) func. = + value , , Mrs 1) ( 1) - x) [ cross mult - v/u(x. +, = = , + + Pz P, X P , P2Xz = + + , P, X P, Pe Expenditure = + - P2Xc , Function : - into BC plug solve for I BC = I - P, X , - (P , X , + p , - Pz) ezVup , R = (F + p, + P2) - Va = I + p , + P = I P P, X Pi Pz pp - , X - , - + zv". eli * = - pi - Pr = F - 2P , X , - P, + Pz = 0 - 28 X1 = I + P, P2 , = P = - x +. -P,it DFT x 0, >I + p  I 9 P 2 prev eq P2 2 plug into = = = · , , , x ,* = 9/4 X- * = 9/y If P, 4 X , 8 = /g * = Xz substitution effect ? I : zv" , p p. -p - P2 /2 I = 2 ( + 9) " u (2) - u -2 [* = 13E - 6 = $12. 38 compensated Demand : Pa · Xz BSlope me X P& becomes Sleeper Da , less oa ot uncompensated you can buy but constant y is Meit X Hicksian = comp demand 2 u(x , xz) = x , + Xz x (p Pc v) BC XzPz o