1 managerial economics demand analysis the concept of elasticity and its applications ch. 3
TRANSCRIPT
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Managerial Economics
Demand Analysis
The Concept of Elasticity
and its Applications Ch. 3
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The concept of elasticity
The sensitivity (degree of responsiveness) of sales (demand) to a change in one of the demand-affecting variables, say, price
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The Importance of Elasticity The firm needs to know the effect of a
change in any of the determinants of demand (price, advertising, income, competitors’ prices, etc.) that affects the demand for a product in order to: Meet sales target Gain market share Maximize profit
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The Price Elasticity of Demand… measures the responsiveness of the quantity demanded to a change in the price of the product, holding constant the values of all other variables in the demand function. In mathematical term,
%in Q Ep = --------------- , ceteris paribus % in P
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The Arc Price Elasticity of Demand
How can the percentage changes in Q and P be calculated in order to derive the price elasticity of demand? Q --------------- (Q1 + Q2)/2 Ep = ------------------ P -------------- (P1 + P2)/2
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Drive the Demand Curve of the following information: (Q = 40,000,000 - 2,500P)
Price
16,000
P2=12,500 B
P1=12,000 A
Q
0 8,750,000 40,000,000
10,000,000
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How sensitive are consumers to a change in the avg. price of automobiles?
We calculate the arc price elasticity of demand between A and B as:
10,000,000-8,750,000------------------------------[10,000,000+8,750,000]/2
Ep = -------------------------------- = - 3.267 12,000 - 12,500 ----------------------- [12,000 + 12,500]/2
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Interpretation Between points A and B (or between the
price range from $12,000 to $12,500), a one-percent increase in the average price of cars will bring about, on average, a reduction of sales by 3.267%, ceteris paribus.
Because the price elasticity of demand is calculated between two points on a given demand curve, it is called the arc price elasticity of demand.
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Classification of The Price Elasticity of Demand
For decision-making purposes, three specific ranges of price elasticity of demand have been identified. Using the absolute value of the price elasticity of demand, the three ranges are:
1) |Ep| > 1, the demand is said to be elastic.
2) |Ep| < 1, the demand is said to be inelastic.
3) |Ep| = 1, we have unitary elasticity.
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Caveat
Elasticity measure depends on the price
at which it is measured.
It is not generally a constant (because
the demand curve is not likely to be a
straight line).
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The Point Price Elasticity of Demand
It measures the price elasticity of demand at a given price or a particular point on the demand curve.
Q Pep = (-----)(----)
P Q
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Calculation of the point elasticity using the demand for automobile equation Q = -2,500P + 1,000I + 0.05Pop - 1,000,000i + 0.05A
Supposing that: P = $12,000, I1 = $23,500, Pop = 230,000,000, i = 10, and A = $300,000,000
Other things being equal,
if P1 = $12,000, Q1 = 10,000,000.
The point price elasticity is:
Q P ep = (-----) (---) P Q
= (-2,500)(12,000/10,000,000)
= - 3
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Point price elasticity (cont.)What's the point elasticity of demand at
P2 = $12,500?
At this price, Q = 8,750,000.
Hence,
Q P ep = (-----) (---)
P Q= (-2,500)(12,500/8,750,000)
= - 3.571
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Two versions of the elasticity of demand – Point vs. Arc
Price
16,000
12,00012,500
ep= -3.571
ep= -3.0Ep= -3.267
8,750,000 10,000,000
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From Concept to Applications We began with a definition of the elasticity of demand based on,
%in Q Ep = --------------- % in P
If we know the price elasticity of demand (Ep), the formula will let us answer a number of "what if" questions.
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Examples(1) How great a price reduction is necessary
to increase sales by 10%?
(2) What will be the impact on sales of a 5% price increase?
(3) Given marginal cost and price elasticity information, what is the profit-maximizing price?
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The price increase needed to reduce gasoline consumption by 1%
Supposing that the elasticity of demand for gasoline is -0.5, how much prices must go up to reduce gasoline use by 1%?
- 0.01- 0.5 = ---------- ,
%P
%P = (-0.01/-0.5) = + 0.02 or 2%
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Price elasticity of demand and Total Revenue - Still Another Application
If |Ep | > 1, i.e., elastic demand,
P, TR decreases
If |Ep | < 1, i.e., inelastic demand,
P, TR increases
If |Ep | = 1, i.e., unitary elasticity,
P, TR remains unchanged.
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Lessons:(1) The first lessons in business: Never lower
your price in the inelastic range of the demand curve. Such a price decrease would reduce total revenue and might at the same time increase average production cost.
(2) When the demand is inelastic, raise the price to increase revenue and, possibly, profit.
(3) When demand is elastic, price increases should be avoided.
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Lessons(4)But should we always cut price
when the demand is elastic? Even over the range where demand is elastic, a firm will not necessarily find it profitable to cut prices; the profitability of such an action depends on whether the marginal revenues generated by the price reduction exceed the marginal cost of the added production.
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Another Example: Optimal PricingStep 1 – Using the relationship between MR and Ep
established in McGuigan/Moyer/Harris, Ch. 3, p. 90
Given, TR = PQ, فقط للفهم
TR (PQ)MR = ------- = --------- Q Q
Q P= P(-----) + Q (-----)
Q Q
Q P 1 = P (1 + ----- -----) = P ( 1 + ----)
P Q ep
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Optimal PricingOptimal Price is when MC = MR
i.e., MC = P (1 + 1/ep)
MCP = ------------- (1 + 1/ep)
That is, the profit-maximizing price is determined by MC and ep
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Determinants of Price Elasticity of Demand
Starter Questions :
(1) If the demand for gasoline is inelastic, why is it that sales at a particular gas station will drop off when it raises prices?
(2) What explains the fact that the demand for some products is more sensitive to price than the demand for other products?
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The determinants are:1. The availability of substitute goods2. The extent to which a good is considered
to be a necessity3. The proportion of income spent on the
product4. The cost of searching for lower prices5. The degree to which price signals quality6. Time
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Differentiation Strategy and Elasticity
If your strategy is to differentiate your product (a costly activity), you need low elasticity (inelastic demand) to enable the higher price.
If you are attempting a low-cost/price leadership strategy, high elasticity is the key. (You need to convince customers that your products are good substitutes for the leading brands.)
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Other ElasticitiesThe income elasticity of demand provides a measure of the responsiveness of demand to changes in income, holding constant the effect of all other variables.
The "arc" income elasticity is:
Q ------------ Q1 + Q2
EI = --------------- I ---------- I1 + I2
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Arc Income Elasticity IllustratedThe Demand for Automobiles:
Q = -2,500P + 1,000I + 0.05Pop - 1,000,000i + 0.05A
Supposing that: P = $12,000, I1 = $23,500, Pop = 230,000,000, i = 10, and A = $300,000,000
Then, Q1 = 10,000,000.
But if income rises to I2 = $24,000, sales forecast is raised by 500,000 to Q2 =10,500,000.
This implies an income elasticity of:
500,000 -------------------------------- 10,000,000+10,500,000
EI = ----------------------------------- = 2.317 500 ------------------------------- 23,500+24,000
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Point income elasticity: Q I
eI = ----- ----- I Q
At I1 = $23,500,
23,500 eI = (1,000) ( ----------------) = 2.35 10,000,000
and at I2 = $24,000,
24,000 eI = (1,000) ( ---------------) = 2.29 10,500,000
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Examples of Income Elasticities
Description Income Elasticity Examples -----------------------------------------------------------------------------------
Inferior goods EI < 0 Basic foodstuffs, (Countercyclical) generic products, bus
rides, etc.
Noncyclical normal 0 < EI < 1 Cigarettes, liquor, goodssoaps, movies, health
care
etc.
Cyclical normal EI > 1 New cars, houses, goodstravel,capital
equipment, etc.
------------------------------------------------------------------------------------------
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Cross-Price Elasticity of Demand
A change in the price of Coca Cola influences the sales of Pepsi. We use the concept of cross-price elasticity of demand to measure the relationship between the price of Coca Cola and the volume of sales of Pepsi.
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The Arc Cross Elasticity of Demand
Supposing that product x and y are related, and that,
Qx = a0 + a1Px + a2I + a3Py
The arc cross-price elasticity is: Qx
-------------- Qx1 + Qx2
EPy = -------------------
Py
------------- Py1 + Py2
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The point cross-price elasticity
Qx Py
e py = ( -----)(----) Py Qx
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Some Uses of Cross-Price Elasticity According to an FTC Report by Michael
Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06
If MCI and other competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?
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Answer
AT&T’s demand would fall by 36.24 percent!
%24.36%
%06.9%4
%4
%06.9
%
%06.9,
dX
dX
dX
Y
dX
PQ
Q
Q
Q
P
QE
YX
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Antitrust and Cross Elasticities of Demand
Cross elasticity of demand is used in industrial organization to measure the interrelations among industries. The case of DuPont and its Cellophane.