Further Equations and Techniques Chapter 3.13-3.17

Economic Applications Supply and Demand Model Linear demand Linear supply Macroeconomic Equilibrium Linear consumption function Linear savings function

Linear Demand Function a relationship between quantity demanded and the market price The relationship is negative since consumers buy less when the price gets higher

Demand and Supply Slope: price sensitivity Intercept: should be positive because consumers will buy something when the price is zerosatiation level

Linear Supply Function A relationship between quantity supplied and the market price The relationship is negative since producers want to sell more at higher prices

Market Equilibrium For the market to be at equilibrium, it is necessary that at the market price quantity demanded be equal to quantity supplied Example Slopes and intercepts: interpretation?

Equilibrium Condition An equilibrium condition: why? When price is below its equilibrium level , we have excess demand. When price is above its equilibrium level , we have excess supply.

Inverse Demand and Supply Functions Economists prefer to put the price on the vertical axis Historical tradition The intercept of the supply function now has economic meaning, whether positive or negative Inverse demand function is the demand function where the price is the dependent variable More quantity in the market (less scarcity) makes prices fall Inverse supply function is the supply function where the price is the dependent variable Economic interpretation is more difficult

Inverse Demand Function

Inverse Supply Function

Demand and Supply Price Demand price is the maximum consumers are willing to pay for the quantity demanded Supply price is the minimum producers are willing to accept for the quantity supplied The results of the analysis do not change!

Equilibrium is the Same! Exercise 3

Economic Modelling Economic model is a simplified form of economic reality Demand and supply functions are examples of behavioral equations (relationships) Equilibrium condition is an example of a conditional equation

Comparative Statics Comparative statics is the analysis of how equilibrium changes when something happens in the economy Taxes Increases in consumer income Changes in prices of the related goods

Excise Tax An excise tax t is the number of dollars that have to go to the government every time a unit is sold Two prices now One price is paid by the buyers, Another price is received by the sellers, Equilibrium condition: There is only one single quantity when this is possible! Notice that now , but !

Excise Tax

Ad Valorem Tax Ad valorem tax is the percentage of the price received by the seller

Macroeconomic Equilibrium Macroeconomic analysis looks at how an economy works as a whole Household income Y must be equal the value of output Q they produce: Output Q must equal aggregate expenditure (demand) E: Combining the two identities, we obtain

Consumption Function Aggregate expenditure E is spread between consumption C and investment I: Consumption function by Keynes says that consumers by more at higher income levels: b>0 because you don’t stop consuming (food) even if your income is zero a>0 as well since consumers buy more with more income a<1 because you don’t spend everything you earn, you save a is referred to as the marginal propensity to consume: it’s the fraction of 1 dollar of income you spend on consumption

Consumption Function

Savings Function Savings is part of consumers’ income Y that they don’t spend on consumption C Substituting for consumption, we obtain the savings function: The value (1-a) is referred to as the marginal propensity to save: it’s the fraction of a dollar of your income you save

A Macroeconomic Model Four equations in five unknowns Y,E,C,I,S However, investment I is an exogenous variable whose value is not determined within the model! Substituting, we obtain: Now we have an equilibrium value of aggregate income Y as a function of: basic consumption b, marginal propensity to consume a, and investment level I Income Y is determined within the model, which is why it is called an endogenous variable

Comparative Statics Suppose I=800, a=0.5, and b=200 Then Comparative statics: imagine that the level of investment increases by 1: I=801 What is going to be the new equilibrium level of income Y? An increase in I by 1 results in an increase in Y by 2: investment multiplier is 2

Comparative Statics: General Case Thus, in the general case, investment multiplier is equal to