Demand and supply: policy analysis and elasticity
4.0 Introduction
In the last chapter, we learnt that demand and supply are powerful tools in the determination of price. Prices fulfill an allocative function in distributing scarce goods between different users or consumers. The present chapter applies demand and supply analysis to a number of practical cases, which are chosen to illustrate the use of price theory and to give practice using it.
4.1 Price controls
Price control or regulations refers to the setting of an upper or lower limit on the price at which a particular product can be bought or sold. An upper limit is a price ceiling and a lower limit is referred to as a price floor.
The objectives of price controls include:
(i) To keep the prices of products at levels which can be afforded by most people especially prices of basic goods such as cooking oil.
(ii) The maintenance of incomes of producers at higher levels than that which would be produced by market forces, e.g.
incomes of farmers.
(iii) To stabilize prices that is to control the persistent increase in the general level o prices.
4.1.1 Price ceiling or maximum price
In October 2001, the government brought back price controls (ceilings) on basic commodities such as bread, mealie-meal, cooking oil, soap and sugar. Those in support of price ceilings argue that they ensure a minimum standard of living to the majority poor who would afford to buy the basic commodities at the controlled price than the market price. However those who oppose the policy argue that it causes shortages.
P2
P0
P1
0 Q2 Q0 Q1 Quantity
Although the equilibrium price is OP0, the government sets a maximum price of OP1. At the maximum price OP1, the quantity demanded (OQ1 exceeds the quantity supplied (OQ2) in other words, there is a shortage of the commodity. Since the price is not allowed to rise above OP1, there is no incentive to increase quantity so as to reduce the shortage. Some suppliers may exit the industry causing the supply curve to shift to the left thus the shortages might be even worse. On the demand side, more of the commodity is consumed than if market prices were charged.
To allocate the limited supply among the many buyers who want to purchase the good, the government may resort to some form of rationing e.g. issuing ration coupons. Frequently, black markets develop under these circumstances, and the commodity is sold illegally at a price higher than the legal maximum. Black marketers would buy OQ2 at the controlled price of OP1. They would sell at the price OP2 which is even higher than the market price OP0.
4.1.2. Price floor or minimum price
A price floor has an opposite effect to that of a price ceiling. It is set at a level above the equilibrium price below which it may not fall. The most common reason for imposing a price floor is to guarantee some minimum income to the supplier of the product. This is the reason why the government imposed price floors on agriculture produce. Similarly, supporters of minimum wage legislation argue that incomes of the poor are raised by introducing a floor below which wages may not fall.
Fig 4.2 The effect of a price floor
Quantity
As is evident, the equilibrium price of the commodity is OP2. Nonetheless, the government sets a minimum price of OPf.At the minimum price, the quantity supplied (OQs) exceeds the quantity demanded (OQd); in other words excess supply will result. Consider a minimum wage policy as an example of the minimum price. At the market wage rate OPe, the level of employment is OQe. With the introduction of the minimum wage at Pf, the demand for labour and the level of employment will fall to OQd. The number of workers who are involuntarily unemployed is QdQs,, that is people who are willing to work in the industry but are not employed.
4.2 Excise tax
Excise tax is a tax levied on expenditure hence it’s a type of indirect taxes. It is levied on goods such as alcohol, spirits and cigarettes. In this case, we will use demand and supply analysis to demonstrate the incidence of such a tax as excise tax. The term 'incidence of taxation' means the individual where the tax falls upon, that is who is legally responsible for paying it. In the case of cigarettes, for example, it can be shared between the producer and the consumer. Consumers usually pay for the tax in the form of a higher price while producers pay in the form of receiving a lower price. The distribution of the tax burden between the consumer and the producer can be determined using demand and supply curves.
Quantity
Suppose that the market demand and supply curves for cigarettes are D and S0respectively, the equilibrium price will be $10 per packet. If the government were to impose an excise tax of $5 per packet, this tax will be collected from the producer hence the cost of production would increase by the same margin. The supply curve will be shifted upward by the amount of the tax, from S0 to St. The posttax price will be $13 per packet - an increase of $3 over its pretax level. Consequently, in this case, $3 of the tax is passed on to consumers, who pay $3 more for a packet of cigarettes. And $2 of the tax is swallowed by the producer, who receives $8 per packet after paying the tax. Therefore the incidence of this tax is such that consumers pay $3 per packet while producers pay $2 per packet of cigarettes.
But, is it always true that producers pass part of the tax on to consumers and absorb the rest themselves? On the contrary, in some cases, consumers may bear almost none of the tax (and producers may bear practically all of it). The result will depend on how sensitive the quantity demanded and the quantity supplied are to the price of the commodity - For example, holding the supply curve constant, the less sensitive the quantity demanded is to the price of the good, the bigger the portion of the tax that that is shifted to consumers.
Fig 4.4Elasticity of demand and the incidence of a tax Price
Quantity
Before tax the price is OP0 regardless of whether D1 or D2 is the demand curve. After the tax, the equilibrium price is OP1if the demand curve is D1, or OP2 if the demand curve is D2. Clearly the increase in the price to the consumer is greater if the quantity demanded is less sensitive to price (D2) than if it is more sensitive (D1).
On the other hand, holding the demand curve constant, the less sensitive the quantity supplied is to the price of the good, the bigger the portion of the tax that is absorbed by producers.
4.3. Elasticity of demand
From the analysis of the effects on price of an excise tax, we noted that market demand curves vary in the sensitivity or responsiveness of quantity demanded to price. The sensitivity or responsiveness to change is what is generally termed elasticity. Elasticity of demand refers to the responsiveness or sensitivity of quantity demanded to changes in:
a) price of the commodity,
b) household disposable income and,
c) prices of other related commodities.
It is from this description that we have the following distinct types of elasticity of demand.
4.3.1. Price Elasticity of Demand (PED)
Price elasticity of demand (PED) measures the degree of responsiveness of the quantity demanded of a commodity to changes in its price. PED is designed to be the percentage change in quantity demanded resulting from one percent change in price. Economists measure PED by the coefficient Ed in this price elasticity formula.
Ed = % change in quantity demanded % change in price
= (Q1 – Q0) x P0
(P1 – P0) Q0
We know from the down sloping demand curve that price and quantity demanded are inversely related. This means that the price elasticity coefficient of demand will always be negative for normal goods. Economists usually ignore the minus sign and simply present the absolute value of the coefficient.
Example
Calculate the price elasticity of demand when a change in price from $400 to $350 lead to an increase in quantity demanded from 800 to 1000 units.
The original P = $400 and change in P = 350 - 400 = -50
The original Q = 800 and change in Q = 1000 - 800 = 200
Ed = 200 x 400
-50 800
= -2
However the coefficient of elasticity is a ratio and the following are important concerning its implications. If:-
1. Ratio is greater that 1, demand is elastic (Ed >1)
2. Ratio is equal to 1 (Ed = 1) demand has unit elasticity (unitary elasticity)
3. Ratio is less than 1 (O< Ed <1 demand="" inelastic.="" is="" o:p="">
4. Ratio is O (Ed = o) demand is perfectly inelastic.
5. Ratio is infinite demand is perfectly elastic.
- These ratios can be represented on diagrams as follows: -
Fig 4.5 Representations of the different elasticties of demand
Price 1) Ed>1 Price 2) Ed=1
0 Q0 Q1 Quantity 0 Quantity
Price 3) Ed<1 u=""> Price 4)Ed=0
0 Q0 Q1 Quantity 0 Q0 Qty 0 Q0 Q1
Demand curves are unlikely to have the same elasticity throughout except were demand curves have unit elasticity, perfectly inelastic or perfectly elastic. Normally, on any demand curve, elasticity of demand will be different at different prices as follows
Fig 4.6 Elasticity along a demand curve
Quantity
The value of elasticity decreases from infinite at point A through unitary at point B to zero at point C. Whether demand for a product is elastic or not will depend on:
(a) Availability of substitutes at the ruling price
The greater the number of substitutes available for a product, the greater will be its elasticity of demand. Also the closer the substitutes are, the greater the elasticity of demand. For example, demand for products like salt and insulin which has no close substitutes is relatively inelastic while demand for margarine which has butter or jam as substitutes tend to be elastic. (b) The proportion of income spent on the product
Demand for goods on which a small proportion of income is spent e.g. match boxes tend to be inelastic while demand for those goods where a larger proportion of income is spent tend to be elastic. Thus the greater the proportion of income which the price of the product represents, the more elastic the demand will tend to be. (c)Addiction or habit forming
Where a product is habit forming e.g. alcohol or cigarettes, this will tend to reduce its elasticity of demand. In extreme cases of addition demand may become perfectly inelastic.
(d) Necessities and luxuries
Demand for luxuries tends to be elastic while that for necessities tend to be inelastic. Necessities are those goods which people can not do without and at the same time can not increase consumption even if price falls. For example, a family which eats three loaves of bread every morning will have to get the same amount in both the event of a price rise and a price fall. Luxuries are goods that people can do without and hence a rise in price may mean that people cut consumption.
4.3.2. Income Elasticity of Demand (YED)
Income elasticity of demand (YED) measures the degree of responsiveness of the quantity demanded of a product to changes in consumer disposable income. The value of income elasticity can be calculated by the following formula.
YED = % change in quantity demanded % change in income
=
|
(Q1 – Q0 )
|
x Y
|
(Y1 – Y0 )
|
Q
|
Categories of income elasticity of demand
These depend on whether goods are normal or inferior.
(a) Positive Income Elasticity (YED>O)
As income increases, demand also increases while decreasing income lead to a decreasing demand. This positive relationship shows that the commodity under consideration is a normal or superior good.
(b) Zero or near zero income elasticity (YED = 0)
In this case, the quantity demanded of a commodity remains constant as income changes. This is typical of basic goods such as salt and cooking oil.
(c) Negative income elasticity (YED <0 span="">
In this case demand falls with a rise in income. The inverse relationship between income and quantity demanded shows that the good in question is an inferior good e.g. black and white TV.
4.3.3. Cross Elasticity of Demand (CED)
Cross elasticity of demand measures the degree of responsiveness of the quantity demanded of one good A to changes in the price of another good B. It is given by the formula.
CED = %change in quantity demanded of A %change in price of B
A positive value shows that the demand for good A rises with a rise in the price of B and indicates that the two goods are substitutes. A negative value indicates that the two goods are complements. A zero value indicates that a change in the price of commodity B will not affect the quantity demanded of commodity A showing that the goods are not related.
Table 4.1 Summary of the coefficients of elasticity
Terminology
|
Value
|
Verbal description
|
Price elasticity of demand
| ||
Perfectly inelastic
|
Zero
|
Quantity demanded does not change as price changes
|
Inelastic
|
Greater than zero but less than one
|
Quantity demanded changes by a smaller percentage than does price
|
Unit elasticity
|
PED = 1
|
Quantity demanded changes by the same percentage as price
|
Elastic
|
1
| |
Quantity demanded changes by larger percentage than does price
Perfectly elastic
PED = Infinite
Buyers are prepared to buy all they can at some price none at any other price.
Income elasticity of demand
Inferior good
YED < 0
Quantity demanded decreases as income increases
Normal good
YED > 0
Quantity demanded increases as income increases
Cross elasticity of demand
Substitute
Positive
Complement
Negative
4.3.4 Application of elasticity of demand concepts
a) Price elasticity of demand and the business person
If a firm faces an inelastic demand curve, then pushing up price will always increase total revenue. Total revenue (TR) or total sales is the amount of money received from the sale of an output. It is given by price multiplied by quantity (TR = P x Q).
If price is increased from P0 to P1, rectangle B shows the revenue that has been given up by increasing the price and rectangle A is the revenue gained. Rectangle A greatly outweigh rectangle B, therefore if demand is inelastic a higher price must be charged in order to maximise the total revenue. Conversely, if demand is elastic, then lowering the price will increase total revenue.
Fig 4.8 Revenue maximization for elastic demand
0 Q0 Q1
Quantity
If demand is elastic, total revenue increases as price falls. Rectangle A will be given up and rectangle B will be gained if price is reduced from P0 to P1. Thus if demand is elastic, reduce the price in order to maximise total revenue.
b) Price elasticity of demand and government policy
Government levies indirect taxes such as value added tax (VAT) and excise duty on expenditure in order to raise revenue. To maximize on revenue collected the government should levy a low tax on goods with elastic demand while laying a high tax on goods with inelastic demand such as alcohol and cigarettes.
c) Price elasticity of demand and monopoly price discrimination
A discriminating monopolist will maximise total revenue by charging high price in the market where demand is inelastic and a low price in the market where demand is elastic. For instance, ZESA tariffs in high and low density residential areas or cell phone peak and off peak call charges.
d) Importance of income elasticity of demand
Income elasticity is used when firms are producing or stocking during business cycles. Business cycles refer to the fluctuations in economic activities through periods of peak, recession, depression, recovery, peak and so on. Superior goods will be produced during recovery and peak periods when real incomes rise while inferior goods are produced during recession and depression periods when real incomes will be decreasing.
4.5 Price elasticity of supply
Elasticity of supply measures the degree of responsiveness of quantity supplied to changes in price. It is the relationship between the proportionate change in price and the associated proportionate change in price and the associated proportionate change in quantity supplied.
The value of elasticity of supply can be calculated by the formula.
Es = %change in the quantity supplied
%change in price
4.4.1. Classification of the coefficient of elasticity of supply
(a) Where the proportionate change in quantity supplied is greater than the proportionate change in price, then supply is
elastic.
(b) Where the proportionate change in quantity supplied is less than the proportionate change in price, then, supply is
inelastic.
(c) Where the quantity supplied does not change as price changes, supply is perfectly inelastic.
(d) Where the quantity supplied is infinity then supply is perfectly elastic.
(e) Where the quantity supplied changes by the same proportionate as does proportionate change in price, then supply has
unitary elasticity.
Graphically, any straight-line supply curve that meets the vertical axis will be elastic and its coefficient of elasticity value will be between one and infinity. A straight-line supply curve that meets the horizontal axis will be inelastic and its coefficient of elasticity value will lie between zero and one. Any straight-line supply curve through the origin will have unitary elasticity.
Fig 4.9 Diagrammatic representations of elasticity of supply
0 Quantity 0 Quantity
0 Quantity 0 Quantity
Price (e) Unitary elastic supply
4.4.2. Determinants of elasticity of supply
a) Elasticity of supply tends to increase with time. In the immediate market period or momentary period, there is insufficient time to change output and so supply is perfectly inelastic. In the short-run, plant capacity is fixed but output can be altered by adding increasing amounts of variable factors. Therefore supply is elastic. In the long run, all desired adjustments including changes in plant capacity can be made and supply becomes still more elastic.
b) The higher the factor mobility, the greater will be the elasticity of supply. That is the ease at which factors or production can be moved from one use to another affect elasticity of supply.
c) The more willing entrepreneurs are to take risks, the greater will be the elasticity of supply.
d) Where suppliers are holding large stocks supply will be elastic.
e) Natural constraints such as drought place restrictions on the elasticity of supply.
4.5 Consumer and producer surplus
Consumer surplus is the difference between what a consumer is willing to pay for a bundle of goods and what he actually pays, which is less. In other words, it is a saving for the consumer. Consider the following example that shows the price a consumer is willing to pay for each successive unit of a good.
Table 4.2 Price schedule
Unit
|
1st
|
2nd
|
3rd
|
4th
|
5th
|
Price
|
$10
|
$8
|
$6
|
$5
|
$2
|
Suppose he buys 4 units. He is willing to pay $10 for the first, $8 for the second, $6 for the third and $5 for the fourth. In total he is willing to pay $29. But when he buys all units at once, he pays only $5 for each unit. This comes to $20. The difference of $9, which he does not pay, is consumer surplus.
Consumer surplus represents welfare gain for consumers because it represents satisfaction gained without having to pay for it.
Refer to the following diagram:
Fig 4.10 Consumer surplus
Price
A
P1
O Q1 Quantity Demanded
For the quantity OQ1, the consumer was willing to pay ABQ1O. But he pays only P1BQ1O. Therefore he saves paying ABP1. When demand for a good is inelastic, the consumer surplus becomes greater.
The producer surplus is the payment made for any product over and above that, which is necessary for the supplier to supply the product.
Fig 4.11 Producer surplus
Price
D
A
B
0 Q0 Quantity
The producer surplus is represented by the shaded triangle ABC.
Maximum prices increase the consumer surplus while minimum prices increase the producer surplus. Thus maximum prices benefit consumers while minimum prices benefit producers.
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