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Open Campus, UWISemester II 2010/11

MANAGERIAL ECONOMICSMGMT2020

2011

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Given: 62 – 63 = 1? Required: Change the position of one of the five numbers to

make the answer correct.

Welcome to MGMT2020, where you are required to think outside the box.

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A Daily Motto

• “Thank God every morning when you get up that you have something to do that day which must be done, whether you like it or not.”

(Charles Kingsley)

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DEMAND FUNCTION[Normal]

• Definition: It shows the relation between all the independent variables and the demand for the main product.

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DEMAND FUNCTION

Deriving the demand function (compressed) with limited information.

Given

Px ($) Qx (unit)

20 400

60 200

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DIAGRAM

P ($)

60

20

200

400 Q

Demand Curve

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Demand Function

TWO–VARIABLE (compressed)

Qx = a + bPx

b = Q/ P = (400 – 200)/20 – 60)

b = 200/(–40) = –5

Qx = a –5Px

a = Qx + 5Px

a = 400 +5(20) = 500

Qx = 500 –5Px (D/F)

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DEMAND CURVE

Definition: It shows the relationship between the price of the main product and quantity demanded, ceteris paribus

The demand curve is also referred to as the inverse demand function

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DEMAND CURVE

Recall: The demand function (compressed) Qx = a + bPx = Qx = 500 – 5Px

The demand curve can be derived from the demand function by making Px to be the subject of the equation.

Px = a + bQx

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DEMAND CURVE

Demand function: Qx = 500 – 5Px

5Px = 500 – Qx

Px = 500/5 – Qx/5

Px = 100 – 0.2Qx (demand curve)

Eye Opener: 26 – 63 = 1

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RELATIONSHIP(D/F and D/C)

Demand function (D/F): Qx = 500 – 5Px

Demand curve (D/C): Px = 100 – 0.2Qx

D/F coefficient (5) is equal to the inverse of the D/C coefficient (1/5 or 0.2).

D/F intercept divided by the intercept of the D/C intercept

(500/100) equals the coefficient of the D/F.

D/C intercept divided by the intercept of the D/F intercept (100/500) equals the coefficient of the D/C.

Please note the coefficients for the D/F and D/C are negative.

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MULTI-VARIABLE DEMAND FUNCTION

DEMAND FUNCTION: Shows the relationship between all the determinants (independent variables) and demand (dependent variable)

Qx = a + bxPx + bsPs + bcPc + byY

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Qx = a + bxPx + bsPs + bcPc + byY

Qx Dependent variable

a Constant (intercept)

b Coefficient (gradient, slope, multiplier)

Px Price for the main product (independent variable)

Ps Price for the substitute (independent variable)

Pc Price for the complement (independent variable)

byY Income (independent variable)

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Qx = a + bxPx + bsPs + bcPc + byY

One coefficient for each independent variable.

Each coefficient measures the change in demand (dependent variable) as a result of a change in an independent variable.

This relationship between a coefficient and its associated variable is only true when all other independent variables are constant (ceteris paribus).

The coefficient (“b”) is derived by dividing the change in the demand (dependent variable) by the change in an independent variable

The coefficients are partial derivates: bx = δQx/δPx bs = δQx/δPs

bc = δQx/δPc by = δQx/δY

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COEFFICIENT

For every one unit change in an independent variable, the dependent variable (Qx) will change by the coefficient of that independent variable.

The sign (+ or –) represents the direction of the change; example, “+” means the dependent variable (Qx) will change in the same direction as the independent variable (they move in the same direction). While “–” means the dependent variable (Qx) will change in the opposite direction as the independent variable (inverse relationship).

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DEMAND ANALYSIS

IllustrationQx = –100 + –10Px + 20Ps –5Pc + 0.5YPx = $100; Ps = $80; Pc = $100; Y = $1,000

For every $1 change in the price of the main product Px (independent variable) the quantity demanded (Qx, the dependent variable ) will change by the coefficient 10 units). Since the sign is “–” if price increase by $1 Qx will decrease by 10 units (and vice versa)

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Qx = a + bxPx + bsPs + bcPc + byY

The price coefficient (bx) will have a negative sign (bx or δQx/δPx <0). The law of demand implies an inverse relationship between the price (Px) of the product and the quantity demanded (Qx).

The price coefficient for the substitute (bs) will have a postive sign (bs or δQx/δPs >0). The price of the substitute (bs) and the demand (Qx) change in the same direction – directly related. Why?

The price coefficient for the complement (bc) will have a negative sign (bcor δQx/δPc <0). The relationship between the price of the complement (bs) and the demand (Qx) is inverse. Why?

The income coefficient could be either postive or negative… (by

or δQx/δY >/<0) Why?

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nQx = a + bxPx + bsPs + bcPc +

byY

Compressed (collapsed) demand function:

Qx = – 100 –10Px + 20(80) –5(100) + 0.5(1,000)

Qx = – 100 + 1,600 –500 + 500 –10Px

Qx =1,500 –10Px

Demand curve refers to the relationship that exists between the quantity demanded of a particular product and the price of that product, with all the other influencing factors held constant. The demand curve is a subset of the demand function where ceteris paribus applies to all of the independent variables except _ _ _ _ _ ?

Deriving the demand curve from the demand function (let Px be the subject of the equation):

10Px = 1,500 – Qx

Px = 1,500/10 – Qx/10

Px = 150 – 0.1Qx (demand curve)

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Demand curve: = 150– 0.1Qx

The demand curve allows us to derive the total revenue (TR) and the marginal revenue curve (MR)

TR is obtained by multiplying price and quantity

TR = P(Q) = (150– 0.1Q)Q

TR = 150Q– 0.1Q2

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MARGINAL REVENUE

MR is found by adding the change in price due to a unit change in quantity to the total revenue. It can also be calculated as TR/Q i.e. the change in total revenue due to a change in quantity demanded: TR = 150Q– 0.1Q2

To calculate MR from an equation you must differentiate

MR = TR/Q = (1)150Q1–1 – (2)0.1Q2–1

MR = 150 – 0.2Q

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ELASTICITY

Regression analysis (RA) measures the consumer responsiveness. However, RA cannot be used to compare consumer responsiveness to products with different units of measurement. The development of elasticity overcame this problem.

Elasticity measures percentage change and not absolute change. We can therefore use two or more products to determine which of them is more sensitive to change.

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PRICE ELASTICITY

The relationship between Px, MR and TR is the price elasticity of demand. The concept of elasticity is used widely in economics and expresses the responsiveness of a dependent variable to a change in an independent (determining) variable.

DEFINITION: The percentage change in quantity demanded (Qx) divided by the percentage change in price (Px)

Px = % change in Qx % change in δPx

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Qx = –100 + –10x + 20sPs –5cPc + 0.5yYPx = $100; Ps = $80; Pc = $100; Y = $1,000

Qx =1,500 –10Px = 1,500 –10(100) = 500

Px = (δQx/ Qx)/(δPx/Px) = (δQx/ Qx)(Px/δPx)

Px = (δQx/ δPx)(Px / Qx) = –10(100/500)

Px = –2

Interpreting price elasticity –Px

The value of the price elasticity is always negative; the law of Demand. Price elasticity is placed in three absolute value classifications.

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CLASSIFICATIONS (ZONES)When [Px] < 1: 1% change in Px will result in less than 1%

change in Qx. This is the inelastic zone; 1% increase in Px will

result in a less than 1% decrease in Qx and an increase in TR. Also,

a 1% decrease in Px will result in a less than 1% increase in Qx and

a decrease in TR

When [Px ] = 1: 1% change in Px will result in a 1% change in Qx. This is the unitary zone; (unitary elastic); 1% increase in Px will result in a 1% decrease in Qx and TR will? Also, a 1% decrease in Px will result in a 1% increase in Qx and TR will?

When [Px] > 1: 1% change in Px will result in a more than 1% change in Qx. This is the elastic zone; 1% increase in Px will result in a more than 1% decrease in Qx and TR will? Also, a 1% decrease in Px will result in a more than 1% increase in Qx and TR will?

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CROSS ELASTICITY Goods can be related in two ways: substitutes and

complements. Changes in the prices of these goods can influence the quantity demanded of the product under consideration.

The economic impact of a substitute and a complementary products on demand can be estimated using cross elasticity of demand

Ps = % change in Qx (substitute)

% change in δPs

or

Pc = % change in Qx (complement)

% change in δPc

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Substitute

Definition: Substitutes are pairs of products between which

the cross elasticity of demand is always positive.

Ps <1; a weak substitute, the markets are not related.

Ps =>1; a strong substitute, the markets are related.

Ps = (δQx/ Qx)/(δPs/Ps) = (δQx/ Qx)(Ps/δPs)

Ps = (δQx/ δPs)(Ps/Qx) = 20(80/500)

Ps = 3.2Are the markets related?

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ComplementDefinition: Complements are pairs of products between

which the cross elasticity of demand is always negative

[Pc] <1; a weak complement, the products are unrelated in consumption (independent)

[Pc ] =>1; a strong complement, the products are related in consumption (interdependent)

Pc = (δQx/ Qx)/(δPc/Pc) = (δQx/ Qx) X (Pc/δPc)

Pc = δQx/ δPc)(Px/Qx = –5(100/500)

Pc = – 1Are the products related?

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INCOME It allows us to classify products as normal (luxuries

or necessities) or inferior goods

It also gives insights into the direction and magnitude of the shift of the demand curve that will follow changes in consumer incomes.

Luxuries: are products that the proportionate change in quantity demanded is greater than the proportionate change in consumer income levels. Elasticity is positive and greater than unitary (1).

In a recession, the proportionate fall in quantity

demanded is greater than the proportionate fall in income levels, while in a boom, the proportionate rise in quantity demanded is greater than the proportionate rise in income levels.

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Necessities: are products that the proportionate change in quantity demanded is less than the proportionate change in consumer income levels. Elasticity is positive but less than unitary (1).

In a recession, the proportionate fall in quantity demanded is less than the proportionate fall in consumer income levels, while in a boom, the proportionate rise in quantity demanded is less than the proportionate rise in consumer income levels.

Inferior: are products that exhibit a negative income effect. Elasticity is negative and less than unitary (1) In a recession income falls and demand will rise, while in a boom income rises demand will fall.

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Y <1 (but greater than 0); a normal good.

Y >1; a luxury good

Y <0; an inferior good

Y = (δQx/ Qx)/(δY/Y) = (δQx/ Qx)(Y/δY)

Y = (δQx/ δY)(Y/Qx) = 0.5(1,000/500)

Y = 1

What type of good?

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ARC ELASTICITYWe have looked at point elasticity Arc elasticity examines the elasticity of demand between two

values.

Arc price elasticity:

Q2 – Q1 X P2 + P1

P2 – P1 Q2 + Q1

Arc cross elasticity:

Qx2 – Qx1 X Ps/c2 + Ps/c1

Ps/c2 – Ps/c1 Qx2 + Qx1

Arc income elasticity:

Q2 – Q1 X Y2 + Y 1

Y2 – Y1 Q2 + Q1

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WAKE UP!1. If marginal revenue is positive, what zone (elasticity)

are you in?

2. If Px= $20; Qx = 400 and px = –2.5, what is the coefficient of the demand curve?

Solution: Px = (δQx/ δPc)(Px/Qx)

δQx/ δPx = Px(Qx/ Px)

δQx/ δPx = –2.5(400/20) = –50 (coefficient of the D/F)

δPx /δQx = 20 /(–2.5)400 = 20/(–1000) = –1/50 δPx /δQx = – 0.02 (coefficient of the D/C)

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What Do You Think?There is wisdom in having “quiet times”,

however, when not properly utilized it will justify the concept that the only negative feedback is…..