Intermediate Microeconomics

Intermediate Microeconomics by Samiran Banerjee

Contents 1. Markets 1.1 Market Demand and Supply 1.2 Determinants of Demand and Supply 1.3 Market Interventions 1.4 Elasticities 2. Budgets 2.1 Commodity Space 2.2 Competitive Budgets 2.3 Changes in Prices or Income 2.4 Non-Competitive Budgets

Contents 3. Preferences 3.1 Binary Relations 3.2 Properties of Binary Relations 3.3 Utility Representation of Preferences 3.4 Types of Preferences 3.5 The Notion of Utility 3.6 Utility, Preferences and Properties 3.7 Special Topics 4. Individual Demands 4.1 Preference Maximization on Budgets 4.2 Calculating Individual Demands 4.3 Two Properties of Demand Functions

Contents 5. Consumer Comparative Statics 5.1 Price and Income Consumption Curves 5.2 Individual Elasticities of Demand 5.3 Decomposing Price Effects 6. Exchange Economies 6.1 The Edgeworth Box 6.2 Properties of Allocations 6.3 Walras Equilibrium 6.4 Allowing for More Goods or Consumers 6.5 Walras’ Law and the Welfare Theorems

Contents 7. Technology 7.1 Production Functions and Productivity 7.2 Types of Technologies 7.3 Returns to Scale 7.4 Production Possibility Frontiers 8. Costs 8.1 Deriving Cost Functions from Technologies 8.2 Cost Concepts 8.3 Returns to Scale Revisited 8.4 Cost Functions with Multiple Technologies 8.5 Deriving Technologies Underlying Cost Functions

Chapter 1 Markets

1.1. Market Demand and Supply ASSUMOTIONS: • a single product (say, the market for steel) • a specific geographical area • relatively short time period, such as a few months.

1.1.1. Plotting a market demand function A market demand function shows how much is demanded by all potential buyers at different prices : dependent variable P: (per-unit price)is the independent variable

…1.1.1. Plotting a market demand function = 120 − 2p where is measured in thousands of tons and p in dollars per ton d/dpis negative

…1.1.1. Plotting a market demand function Figure1.1 Marketdemand Law of Demand’: keeping all other factors fixed, as the price of a product increases, its quantity demanded decreases.

…1.1.1. Plotting a market demand function inverse market demand: economists customarily put p on the vertical axis and on the horizontal axis. p = 60 − This tradition follows Alfred Marshall’s classic text, Principles of Economics, which was published in 1890. • Slope: –0.5

1.1.2 Aggregating demand functions market demand curve for steel in the US: = 100 − p demand for steel in the rest of the world (ROW): = 150 − p corresponding inverse demand curves: p= 60 − & p= 45 −

…1.1.2 Aggregating demand functions = 0 > 0 45 ≤ p < 60: 0 ≤ p < 45: > 0 > 0 Figure 1.2 Aggregate demand

…1.1.2 Aggregating demand functions The aggregate demand is given by the horizontal sum of the US and ROW demands: + = 250 − 5p Figure 1.2 Aggregate demand

…1.1.2 Aggregating demand functions 250 − 5p if 0 ≤ p < 45 100 − 5/3 p if 45 ≤ p ≤ 60 inverse aggregate demand: 60 − 0.6 if 0 ≤ ≤ 25 50 − 0.2 if 25 < ≤ 250 Figure 1.2 Aggregate demand

1.1.3 Plotting a market supply function S(p) is the quantity supplied by all the sellers in this market at the price p. Ass. the world supply curve: 5p So: inverse world supply: p =

…1.1.3 Plotting a market supply function Intersection: = $25 = 125 Figure 1.3 Market equilibrium

1.1.4 Market equilibrium A market is said to be in equilibriumif there is a price, p∗, at which the quantity demanded equals the quantity supplied = D() = S() is equilibrium price and is equilibrium quantity

…1.1.4 Market equilibrium Stable equilibrium: Any deviation from equilibrium will be automatically redressed by market forces to restore the price back to its equilibrium level

…1.1.4 Market equilibrium At= $30 excess supply = 50 So: buyers are willing to buy So: excess supply exerts downward pressure on the market price back towards the equilibrium price of $25 Figure 1.3 Market equilibrium

…1.1.4 Market equilibrium At= $15 excess demand = 100 So: buyers are willing to buy So: shortage of the product exerts upward pressure on the market price towards the equilibrium price, Figure 1.3 Market equilibrium

1.1.5. Consumer and producer surplus In any voluntary transaction between a buyer and a seller, trade takes place at some price between the maximum price a buyer is willing to pay and the minimum price a seller is willing to accept • individual consumer surplus: Thedifferencebetweena buyer’s maximum price and the actual price paid • individual producer surplus: The difference between the price received by a seller and the minimum price this seller is willing to accept

...1.1.5. Consumer and producer surplus The sum of consumer and producer surpluses is a measure of the gains from trade in this market and re- garded as an index of market efficiency Figure 1.4 Consumer and producer surplus

1.2 Determinants of Demand and Supply • The market demand for any product depends on several variables other than the price of that product • (a) The income levels of potential buyers, • (b) The prices of other goods, • (c) The tastes or preferences of buyers, and • (d) The number of buyers • A change in any of these couses a shiftin market demand curve

...1.2 Determinants of Demand and Supply • A good with a positive income effect is called a normal good • A good with a negative income effect is called an inferior good. • An increase in the price of a substitute good would make consumers buy more of the good • An increase in the price of a complement is likely to cause a decrease in the demand for this product

1.3 Market Interventions 1.3.1 Price ceilings • Is a maximum price imposed on a particular product • The sellers have to engage in rationing • Leads to a market disequilibrium • Aria C shows the deadweightlossof a price ceiling

...1.3 Market Interventions 1.3.2 Price floor • Is a minimum price imposed on a particular product • Leads to a market disequilibrium • Aria C shows the deadweightlossof a price floor

...1.3 Market Interventions 1.3.3 Quotas • A quota is a maximum quantity limit imposed on a particular product • For a quota to be effective, the quantity limit has to be less than the original market equilibrium quantity.

...1.3 Market Interventions 1.3.4 Taxes • Taxes may be either per-unitor ad valorem, and imposed on either sellers or buyers. • Per-unit tax:Fixed dollar amount for each unit traded. • Ad valorem: Tax on the value of a sale.

...1.3 Market Interventions A per-unit tax on sellers • Sellers earned $10 on each unit sold previously, but now they earn 14 − 6 = $8 net of taxes, i.E., $2 less than before. • This $2 is the incidence of the tax on sellers. • The price difference of 14 − 10 = $4 is called the incidenceof the tax on buyers. A per-unit tax on sellers • Suppose a tax, t, of $6 per unit is imposed on sellers. • Then, each seller will raise the minimum price she is willing to accept by the amount of this tax, thereby shifting the inverse supply curve up by $6 at each point

...1.3 Market Interventions A per-unit tax on Buyers • Buyers have to pay 8 + 6 = $14 to purchase one unit of the good, while sellers receive $8 for each unit sold. • Thus the incidence of the tax on buyers is still $4 while that on sellers is still $2.T. A per-unit tax on Buyers • Suppose the tax of $6 had been imposed on buyers instead of sellers. • Since buyers have to pay the tax after they purchase the product, each buyer will lower her maximum price by the amount of the tax • Thereby shifting the demand curve down by $6 at each point.

Intermediate Microeconomics