Law of Demand

• A decrease in the price of a good, all other things held constant, will cause an increase in the quantity demanded of the good.

• An increase in the price of a good, all other things held constant, will cause a decrease in the quantity demanded of the good.

Change in Quantity Demanded

Quantity

Price

P0

Q0

P1

Q1

An increase in price causes a decrease in quantity demanded.

Change in Quantity Demanded

Quantity

Price

P0

Q0

P1

Q1

A decrease in price causes an increase in quantity demanded.

Changes in Demand

• Change in Buyers’ Tastes

• Change in Buyers Incomes– Normal Goods– Inferior Goods

• Change in the Number of Buyers

• Change in the Price of Related Goods– Substitute Goods– Complementary Goods

Change in Demand

Quantity

Price

P0

Q0 Q1

An increase in demand refers to a rightward shift in the market demand curve.

Change in Demand

Quantity

Price

P0

Q1 Q0

A decrease in demand refers to a leftward shift in the market demand curve.

Law of Supply

• A decrease in the price of a good, all other things held constant, will cause a decrease in the quantity supplied of the good.

• An increase in the price of a good, all other things held constant, will cause an increase in the quantity supplied of the good.

Change in Quantity Supplied

Quantity

Price

P1

Q1

P0

Q0

A decrease in price causes a decrease in quantity supplied.

Change in Quantity Supplied

Quantity

Price

P0

Q0

P1

Q1

An increase in price causes an increase in quantity supplied.

Changes in Supply

• Change in Production Technology

• Change in Input Prices

• Change in the Number of Sellers

Change in Supply

Quantity

Price

P0

Q1Q0

An increase in supply refers to a rightward shift in the market supply curve.

Change in Supply

Quantity

Price

P0

Q1 Q0

A decrease in supply refers to a leftward shift in the market supply curve.

Market Equilibrium

• Market equilibrium is determined at the intersection of the market demand curve and the market supply curve.

• The equilibrium price causes quantity demanded to be equal to quantity supplied.

Market Equilibrium

Quantity

Price

P

Q

D S

Market Equilibrium

Quantity

Price

P0

Q0

D0 S0

Q1

P1

D1

An increase in demand will cause the market equilibrium price and quantity to increase.

Market Equilibrium

Quantity

Price

P1

Q1

S0

Q0

P0

D0D1

A decrease in demand will cause the market equilibrium price and quantity to decrease.

Market Equilibrium

Quantity

Price

P0

Q0

D0 S0

Q1

P1

An increase in supply will cause the market equilibrium price to decrease and quantity to increase.

S1

Market Equilibrium

Quantity

Price

P1

Q1

D0

Q0

P0

A decrease in supply will cause the market equilibrium price to increase and quantity to decrease.

S1 S0

Concept of the Derivative

The derivative of Y with respect to X is equal to the limit of the ratio Y/X as X approaches zero.

0limX

dY Y

dX X

Rules of Differentiation

Constant Function Rule: The derivative of a constant, Y = f(X) = a, is zero for all values of a (the constant).

( )Y f X a

0dY

dX

Rules of Differentiation

Power Function Rule: The derivative of a power function, where a and b are constants, is defined as follows.

( ) bY f X aX

1bdYb aX

dX

Rules of Differentiation

Sum-and-Differences Rule: The derivative of the sum or difference of two functions U and V, is defined as follows.

( )U g X ( )V h X

dY dU dV

dX dX dX

Y U V

Rules of Differentiation

Product Rule: The derivative of the product of two functions U and V, is defined as follows.

( )U g X ( )V h X

dY dV dUU V

dX dX dX

Y U V

Rules of Differentiation

Quotient Rule: The derivative of the ratio of two functions U and V, is defined as follows.

( )U g X ( )V h X UY

V

2

dU dVV UdY dX dXdX V

Rules of Differentiation

Chain Rule: The derivative of a function that is a function of X is defined as follows.

( )U g X( )Y f U

dY dY dU

dX dU dX

Optimization With Calculus

Find X such that dY/dX = 0

Second derivative rules:

If d2Y/dX2 > 0, then X is a minimum.

If d2Y/dX2 < 0, then X is a maximum.