II.    Demand

 

A. What is demand?

 

   Demand is a schedule which relates the quantities demanded for a product to its prices.

 

B. What is the money income constant demand?

 

   It is the demand curve derived when holding money income constant.

 

C. How to calculate the relative price of a commodity?

 

 Price is always relative price in Mircoeconomics.

 

1) How to calculate the relative price?

 

Given: Nominal price of an apple = $4

     Nominal price of an orange = $2

                               

        Then:        Relative price of an apple  =      Price of apple/price of orange

           =      $4/$2

                                                                    =      2

                 Relative price of an orange        =      Price of orange/price of apple

            =      $2/$4

                                            =      1/2

 

D. What is the first law of demand?

 

The first law of demand asserts that when the relative price of a commodity increases, its quantity demanded decreases, and vice verse.

 

The first law of demand is an assertion or an empirical law.

 

The Law of demand can be expressed by a downward sloping demand curve. That means, the higher the price, the smaller the quantity demanded is.

 

Since the quantity demanded for a commodity is not observable, the law of demand cannot be directly tested. We have to derive testable implications from the law.

 

E. What is Alchain’s generalization about the first law of demand?

 

According to Alchain, if the prices of both good X and good Y changed by the same absolute amount, the relative of price of both goods change too. The law of demand predicts that more of the relatively cheaper good will be consumed.

 

For example:

What will happen to the relative prices of the grapes after their arrival in Hong Kong? Which kind of grapes becomes relatively cheaper? Which kind of grapes will an individual consume?

 

	Price/Kg in California	Shipment costs/Kg (same absolute amount)	Price/Kg in Hong Kong
Choice Grapes	$20	$2	$22
Standard Grapes	$10	$2	$12

 

                In California:     Nominal price of choice grapes =      $20

Nominal price of standard grapes      =      $10

 

Relative price of choice grapes  =      $20/$10  =  2

Relative price of standard grapes =    $10/$20  = 0.5

 

In Hong Kong:  Relative price of choice grapes  =      $22/$12   =      1.8

Relative price of standard grapes       =     $12/$22   =      0.54        

Choice grapes become relatively less expensive in Hong Kong. And according to the law of demand, other things being equal, relatively more choice grapes will be consumed by consumers in Hong Kong

 

F. Alchain’s further generalization about the first law of demand?

 

According to Armen Alchain, given 2 prices P₁ and P₂ of good 1 and good 2 respectively (with P₁>P₂), if a fixed sum, S is added to both prices, then the price of good 1 becomes relatively less expensive. That is (P₁ + S)/( P₂ + S) < P₁/ P_2.

 

Moreover, given 2 prices P₁ and P₂ of good 1 and good 2 respectively (with P₁>P₂), if a fixed sum, S is subtracted from both prices, then the price of good 1 becomes relatively more expensive. That is (P₁ – S)/( P₂ – S) >      P₁/ P₂.

 

For example:

 

Given:   Nominal price of choice grapes = $20

Nominal price of standard grapes = $10

 

      Then:    Relative price of choice grapes  =      $20/$10   =      2

Relative price of standard grapes       =      $10/$20   =      0.5

 

If a fixed amount of $5 is subtracted.

 

Then:          Relative price of choice grapes  =      ($20 - $5)/(10 - $5) = 3

Relative price of standard grapes       =      ($10 - $5)/($20 - $5)= 1/3

 

G. Price Elasticity of Demand (Sd)

 

1) What is price elasticity of demand?

 

Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price.

 

 

Sd   = － (% Δ Qd)/(% ΔP)

        = － (ΔQd/ΔP) x (P/Qd)

                       

If the absolute value of elasticity of demand is greater, it is more elastic. Elasticity measures proportionate changes, not absolute change.

 

2) What are the types of price elasticity of demand?

 

a) Elastic demand (∞＞Sd＞1)

 

Demand is elastic when the percentage change in the quantity demanded is greater than the percentage change in price. A certain percentage change in price will lead to a more than proportionate change in the quantity demanded.

 

b) Inelastic Demand (1＞Sd＞0)

 

Demand is inelastic when the percentage change in the quantity demanded is smaller than the percentage change in price. A certain percentage change in price will lead to a less than proportionate change in quantity demanded.

 

                        c) Perfectly elastic demand (Sd =∞)

 

Demand is perfectly elastic when a change in price will lead to an infinite change in quantity demanded. The demand curve is a horizontal straight line.

 

d)     Perfectly inelastic demand (Sd = 0)

 

Demand is perfectly inelastic when the quantity demanded remains constant when price changes. The demand curve is a vertical line.

 

       e)     Unitary elastic demand (Sd = 1)

 

Demand is unitary elastic when every percentage change in price is matched by the same percentage change in the quantity demanded. A certain percentage change in price will lead to the same percentage change in quantity demanded.

 

The demand curve is a rectangular hyperbola with the area under the curve (i.e. P x Q) = TR which is a constant.

 

3) Price Elasticity on a Straight Line Demand Curve/Linear Demand Curve

 

a) Price elasticity varies along a demand curve

 

At the vertical intercept, price elasticity is infinity because the value of Qd is very small and approaches 0 and so P/Qd becomes very large and approaches infinity.

 

At the horizontal intercept, price elasticity is 0 because the value of P is very small and approaches 0 and so P/Qd becomes very small and approaches 0.

 

b) Measuring price elasticity at a point on the demand curve

 

Let’s measure the Sd of point C.

 

Sd of point C = － (ΔQd/ΔP) x (P/Qd)

= － (P/Qd) /(ΔP/ΔQd)

                               

                                ∵    ΔP/ΔQd        = slope of demand curve = AB/BC = AB/0D

                                        P/Qd                = 0B/0D

                                ∴   Sd of point C   = (0B/0D)/(AB/0D) = 0B/AB

 

That is Sd of a linear demand curve is the ratio of the price to the distance between the price and the y-intercept.

 

c) Comparing the Sd of different demand curves

                               

i) If 2 straight-line demand curves has the same slope, the one nearer to the origin is more elastic at any given price

 

Since                Sd D₁＝0 P₁/AP₁

                        Sd D₂＝0 P₁/B P₁

                        B P₁＞AP₁

 

Then         Sd D₁＞Sd D₂

 

That is             D₁ is more elastic

 

ii)     If 2 linear demand curves intercept, the flatter one is more elastic at the point of intersection.

 

Since                Sd D₁＝0 P₁/BP₁

                        Sd D₂＝0 P₁/AP₁

                        B P₁＞AP₁

                                       

Then         Sd D₂＞Sd D₁

 

That is D₂ is more elastic at the point of intersection.      

 

       

iii)     If 2 linear demand curves intercept, the flatter one is more elastic.

 

Since D₁ has a higher vertical intercept than D₂. That is, B is always higher than A, D₁ is less elastic than D₂ at every price

 

 

iv)    If 2 linear demand curves have the same vertical intercept, the price elasticity of the 2 demand curves are the same at any given price.

 

Since                Sd D₁＝OP₁/P₁A

                        Sd D₂＝OP₁/P₁A

Then         Sd D₁＝Sd D₂

That is              D₁ and D₂ have the same elasticity

       

                        

H.         What are the relationship between price, price elasticity of demand and total revenue?

 

1)     Elastic Demand

 

Price increases will lead to a decrease in TR and vice versa.

 

                2)     Inelastic Demand

 

Price increases will lead to an increase in TR and vice versa.

 

3)       Unitary Elastic Demand

 

When the price of the commodity changes, there will be no change in its TR.

 

                4)     Perfectly Elastic Demand

 

If the price of a commodity is a constant, then an increase in its quantity demanded will increase TR and vice versa.

 

                5)     Perfectly Inelastic Demand

 

If the quantity demanded is a constant, then an increase in price of the commodity will increase its TR and vice versa.

 

 

I.            What are the factors affecting price elasticity of demand?

 

1)          The availability of substitutes

 

If a good has a large number of substitutes, it is more elastic and vice versa.

 

2)          Necessities and luxuries

 

Necessity refers to a normal good which income elasticity is smaller than 1. If there is a change in price, the change in quantity demanded is smaller for a necessity.

 

Luxury refers to a normal good which income elasticity is greater than 1.

 

3) The Second Law of Demand

 

The longer the time allowed to adjust the quantity demanded for a commodity in response to a price change, the greater the price elasticity. Price elasticity of demand is greater in the long run. It is because the longer the time period, the larger is the substitution away from higher priced commodity. Immediate response to price changes is very costly as it is costly to search the market for substitutes or alternatives within a short time period. It is cheaper to delay responses to price changes.

 

The second law of demand is not generally accepted by all economists.

 

J.      What is total revenue (TR)?

 

TR = P x Q

 

          K.     What is average revenue (AR)?

 

AR = TR/Q = (P x Q)/Q = P

The AR curve coincides with demand curve.

 

L.       What is marginal revenue (MR)

 

        MR = ΔTR/ΔQ

 

It is the amount added to the total revenue by addition of one unit of commodity sold.

 

        M.    What is the relationship between TR, AR, MR and demand?

 

Price	Quantity Demanded	Total Revenue (P x Q)	Average Revenue (TR/Q)	Marginal Revenue
10	3	30	10	8
9	4	36	9	6
8	5	40	8	4
7	6	42	7	2
6	7	42	6	0
5	8	40	5	-2
4	9	36	4	-4
3	10	30	3	-6
2	11	22	2	-8
1	12	12	1	-10

 

1)     

Example:

 

TR of 4 units = $36 = MR of 1^st unit ($12) + MR of 2^nd unit ($10) + MR of 3^rd unit ($8) + MR of 4^th unit ($6)

 

2)     When demand is downward sloping, MR＜P. MR is a straight line curve and always lies below demand curve (or AR curve).

 

Reason:

 

Units	P/unit	TR	Remarks
5	$8	$40	Ø            If the seller wants to sell more, he has to reduce price.
6	$7	$42	Ø            If the seller reduces price from $8 to $7, there is $2 increase in TR when 1 additional unit is sold. Ø            That is MR = $2, but per unit price $7, so MR＜P.

Note        :

 

In order to sell the 6^th unit, the seller has to reduce the price of the previous 5 units.   

• Previously:         @$8 for 5 units
• Now:                 @$7 for 5 units; $7 for 6^th unit
• That is:         For the 1^st 5 units, losing $1 for each unit. That is
• there is a total loss of $5. For the 6^th unit, there is a gain of $7. So

MR = $7 – $5 = $2

 

                             

       

                   

4)     Relationship between TR, AR and MR

 

             a)     The area under MR curve up to any point is equal to the TR curve at that point.

b)     When MR is positive, TR curve rises

c)     When MR=0, TR is at maximum

d)     When MR is negative, the TR curve falls

 

        N.    What is the relationship between price elasticity of demand and total revenue?

 

                1)     In terms of Diagram:

                     

                     2) In terms of Formula: MR = P[1+(1/Sd)]

 

a)     Unitary Elastic: (Sd = -1)

MR = P[1+(1/-1)]

MR = P(0)

MR = 0

 

 

                        b)     Elastic: (∞n＜Sd＜-1)

Let Sd = -2

MR = P[1+(1/-2)]

MR = P(0.5)

MR = 0.5P

 

Since P is always positive, then 0.5P is positive, so MR＜P and MR＞0.

 

                        c)     Inelastic: (0＞Sd＞-1)

LetSd = -0.2

MR = P[1+(1/-0.2)]

MR = P(1-5)

MR = -4P

 

Since P is always positive, then –4P is negative, so MR＜P and MR＜0.

 

                        d)     Perfectly Elastic: (Sd = -∞)

MR = P[1+(1/-∞)]

MR = P(1 – a very small number)

MR = P

 

                        e)     Perfectly inelastic: (Sd n =0)

Meaningless to talk about MR because the quantity does not change.

 

        O.    What is income elasticity of demand (Si)?

 

Income elasticity of demand is measured by what percentage an individual will increase his consumption of a commodity when his income is increased by one percent.

 

        P.     How to calculate income elasticity of demand (Si)?

                        = (ΔQd/ΔY) x (Y/Qd)

 

        R.     What are the values of income elasticity of demand (Si) for various goods?

 

                1)     Normal Good: Si＞0 (That is positive)

• The Engel’s curve has a positive slope.
• An increase in income will lead to an increase in quantity demanded and vice versa.

2)       Luxury Good: Si＞1

• The consumption of a commodity is quite responsive to income in the sense that a percentage increase in income leads to a greater percentage increase in consumption.
• Example:
• If income increases from $8 to $12. (A 50% increase)
• Consumption of Commodity X increases from 6 to 12 units. (A 100% increase)

 

                3)     Inferior Good: Si＜0 (That is negative)

• The Engel’s curve has a negative slope.
• An increase in income will lead to a decrease in quantity demanded and vice versa.

 

        S.     What is the relationship between income elasticity of demand for all commodities?

 

• Given a certain change in income, a more than proportional change in the consumption of one commodity implies a less than proportional change in the consumption of at least one other commodity.
• Thus, the average income elasticities of demand for all commodities must add up to one.

 

• Reason:
• Assumption:
• All money income is spent on Commodity X and Commodity Y only
• Px = price of Commodity X, which is a constant.
• Py = price of Commodity Y, which is a constant.
• Qx = quantity demanded of Commodity X
• Qy = quantity demanded of Commodity Y
• Proof:

I = (Px x Qx) + (Py x Qy)

                                ΔI = (Px xΔQx) + (Py xΔQy)

                                ΔI/ΔI = (Px xΔQx/ΔI) + (Py xΔQy/ΔI)

                1= (Px xΔQx/ΔI) + (Py xΔQy/ΔI)

                                           1= (Px xΔQx/ΔI x Qx/Qx x I/I ) + (Py xΔQy/ΔI x Qy/Qy x I/I)

                                          1= (PxQx/I x ΔQx/ΔI x I/Qx ) + (PyQy/I ΔQy/ΔI x I/Qy)

• Whereas:
• PxQx/I and PyQy/I are the percentage of income spent on Commodity X and Commodity Y respectively.
• ΔQx/ΔI x I/Qx andΔQy/ΔI x I/Qy) are the income elasticities of demand for Commodity X and Commodity Y respectively.
• Thus:
• The weighted average of income elasticities of demand for all commodities purchased by an individual at a given level of income must be equal to 1.
• Example:
• Assumption:
• Income = $1000
• Price of a dog = $10
• Consumption of hot dog = 40 pieces
• Income elasticity of hot dog = 0.7
• Price of a CD = $60
• Consumption of CD = 10 pieces
• Income elasticity of CD = 1.2
• Thus:
• % of income spent on hot dog = ($10x$40)/$1000 x 100% = 40%
• % of income spent on CD = ($60x$10)/$1000 x 100% = 60%
• If income increases by 50%

 

• Then:
• New income = $1000 x 1.5 = $1500
• Increase in hot dog consumption = 0.7 x 50% = 35%
• New hot dog consumption = 40(1+35%) = 54 pieces
• Income spent on hot dog = $10 x 54 pieces = $540
• Increase in CD consumption = 1.2 x 50% = 60%
• New CD consumption = 10(1+60%) = 16 pieces
• Income spent on CD = $60 x 16 pieces= $960
• 1 = (0.4 x 0.7) + (0.6 x 1.2)
• If we assume all income is spent, then on average, a 1% increase in income will yield a 1% increase in total purchase.
• It implies that whatever one particular commodity is inferior, there must be at least a normal good to offset the inferior good so that the average income elasticity of demand equals to 1.
• Income elasticity is important to firms in estimating sales for their products.
• Firms expecting recession and falling income may introduce product lies that produce commodities that are believed to be inferior in nature.

 

        T.     What is cross elasticity of demand (Sc)?

 

• Cross elasticity is the proportional change in quantity demanded of  Commodity X in response to a proportional change in the price of another commodity Y.

 

        U.    What is the formula of cross elasticity of demand (Sc)?

 

Ø            

        V.     What are the values of cross elasticity of demand (Sc) for various goods?

 

• If Commodity X and Commodity Y are substitutes: Sc＞0 (That is positive)
• If Commodity X and Commodity Y are complements: Sc c＜0 (That is negative)