1. Further Equations and Techniques
Chapter

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

3. 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

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

5. 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

6. 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?

7. 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.

8. 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

9. Inverse Demand Function

10. Inverse Supply Function

11. 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!

12. Equilibrium is the Same!
Exercise 3

13. 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

14. 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

15. 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 !

16. Excise Tax

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

18. 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

19. 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

20. Consumption Function

21. 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

22. 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

23. 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

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