It is now time to develop some technical concepts that will
be useful in later analysis. The first of these is the concept
of elasticity. Until now we have described the shapes of demand
and supply curves in terms of their slopes. **It is not always
meaningful to describe curves as flat or steep, because whether
a curve appears flat or steep depends upon the units in which
price and quantity are measured.**

The slope of the demand curve is shown in Figure 1. Let Δ represent the words "small change". We can then express the slope of the demand curve, denoted by the greek symbol δ, as

1. δ = ΔP /ΔQ

Measure the quantity of eggs in dozens and the price of eggs in dollars. If, say, a rise in price of $1.00 reduces egg consumption by 5 dozen as we move up along the demand curve, the slope will be -0.2.

Now suppose that we measure the quantity in numbers of eggs
and the price in dollars as before. The same demand curve will
now be flatter---a rise in the price of $1.00 will reduce egg
consumption by 60 eggs, yielding a slope equal to -0.016667.
If, alternatively, we were to measure the price of eggs in cents
and the quantity of eggs in dozens, the slope of this same
demand curve would then be -100/5 = -20. **The apparent slope of the
line on the graph will depend as well on how widely we space the
units of price and quantity along the axes**---if, for example, the
quantity units are spaced a quarter of an inch apart the curve will
appear steeper than if they are spaced half an inch apart.

**By measuring the responsiveness of quantity to changes in
price using the concept of elasticity, we avoid this dependence
on units of measurement. The elasticity of demand is defined as
the relative change (or percentage change) in quantity divided
by the relative (or percentage) change in price.** Let us use the
greek symbol Φ to denote the elasticity of demand. Then we can
write

2. Φ = ( ΔQ / Q ) / ( ΔP / P )

Since dividing by a number is equivalent to multiplying by its reciprocal we can rewrite the above equation as

3. Φ = ( ΔQ / Q ) ( P / ΔP ) = ( ΔQ / ΔP ) ( P / Q )

Since the slope of the demand curve is equal to the change in price divided by the change in quantity, the term ( ΔQ / ΔP ) in the above equation is the reciprocal of the slope. Then we can write Equation 3 as

4. Φ = ( ΔQ / ΔP )( P / Q ) = ( 1 / δ )( P / Q )

**The elasticity is the reciprocal of the slope multiplied by the
ratio of price over quantity.** All this is illustrated in Figure 2 where
the elasticity of demand is measured relative to the initial price-quantity
combination ( P_{0},Q_{0} ) . It
turns out that the elasticity will not be constant as we move along the curve.
As should be clear from Equation 4, given a constant slope, **the elasticity
will decline as P / Q declines as we move down to the right along
the straight-line demand curve---at the vertical axis where Q is
zero the elasticity is infinite and at the quantity axis where P
is zero the elasticity is zero.**

As shown in Figure 3 below, **the elasticity of supply
is calculated in exactly the same
way as the elasticity of demand---the only difference is that the
elasticity of supply is positive while the elasticity of demand
is negative, reflecting the fact that the supply curve is upward
sloping and the demand curve negatively sloped.** We denote the
slope of the supply curve by θ in the figure and measure the
elasticity relative to the initial price-quantity combination
( P_{0} , Q_{0} ) .
**The elasticity will not be constant as we move up along a straight-line
supply curve unless that line passes through the origin, in which case both
the slope and the ratio P / Q will be constant.**

The total revenue to the seller of a commodity, or total
expenditure by the purchaser, is obtained by multiplying the
price by the quantity. It appears in Figure 4 as the area of a
rectangle whose bottom left corner is the origin and top right
corner is a point on the demand curve. The top left and bottom
right corners equal price and quantity respectively. The shaded
rectangle in Figure 4, for example, gives the total revenue at
point **c** on the demand curve---the product of the
price P_{0} and the quantity Q_{0}. The
total revenue at point **a** is the rectangle
P_{1}** a** Q_{1} **0**.

It is also clear in the above Figure that the total revenue varies
as we move along the demand curve. **The total revenue at zero
quantity and price P _{m} is zero. As we
move down along the demand curve, the total revenue increases, reaching
its maximum at the point b (which is middle-distant
from the two ends of the curve) and then declines, reaching zero again at
price zero and quantity Q_{m}.
**

**
Total revenue is portrayed in the Figure as the inverted parabola
0 g m h Q_{m} ---it is measured on a different scale on
the vertical axis, of course, than is the price.** The shaded area
P

**Marginal revenue is defined as the change in total revenue
that occurs when we change the quantity by one unit.** We can
express the marginal revenue, denoted by MR, as

5. MR = ΔTR / ΔQ

where TR is total revenue. The **marginal revenue is thus the
slope of the total revenue curve** in Figure 5. **At quantity zero, the
marginal revenue is equal to the price---selling the first unit adds
one times the price of that unit to the total revenue. As quantity increases
the marginal revenue falls because as we add successive units
not only is the price of the last unit lower than the price of
the previous unit but all previous units have to be sold at this
lower price.**

Marginal revenue for each quantity sold is given in Figure 5
as the distance between the thick line and the horizontal axis
at that quantity. This distance is equal to the slope of the
total revenue curve at that quantity. **At the point of maximum
total revenue m the slope of the total revenue
curve is zero and the marginal revenue is therefore also zero. The
marginal revenue curve thus crosses the horizontal axis at the quantity
at which the total revenue is maximum. When the demand curve
is a straight line, this occurs at the middle point of the curve,
at a point on the horizontal axis that bisects the
distance 0 Q_{m}. **
Past the mid-point of a straight line demand curve, the marginal
revenue becomes negative.

Why is marginal revenue important? This question is best
answered by way of example. Consider the market for fresh eggs
in a locality. Suppose that the government permits producers to
establish an Egg Marketing Board with the power to set the price
of eggs to the consumer and allocate output quantities to all
individual producers. Purchases of eggs from outside the local
area are prohibited. This situation is shown in Figure 6. The
demand curve is given by the line DD and the supply
curve is the horizontal line C_{0}S. A horizontal
supply curve is a reasonable assumption here
because most of the inputs used to produce eggs can be purchased
by egg producers at fixed market prices---these inputs are used by
other industries and producers of eggs use a small fraction of the
available supply. This implies that chicks can be hatched and
raised to hens at constant cost.

Egg producers like this arrangement because it enables them to sell their eggs to consumers at a price above the cost of production, yielding a profit indicated by the shaded area in Figure 6. The problem faced by the Marketing Board, acting on their behalf, is to determine the quantity level that will maximize that profit. At a lower output quota there is a gain from a higher price, but the quantity producers sell will be less.

The profit is the excess of total revenue, given by the
area P_{1} **a** Q_{1} **0**, over
total cost, given by the
area C_{0} **b** Q_{1}0. At
every quota level the Board's problem is to decide whether to
increase the output quota by one unit. It will do this if the
additional revenue from selling another unit to consumers---the
marginal revenue---is greater than the additional to
total cost from producing another unit---called the marginal
cost.

The marginal revenue is given by the thick line in Figure 6. The
marginal cost is given simply by the horizontal supply
curve---each additional unit produced adds **0** C_{0}
to total cost. **Starting from zero, therefore, the Board will increase the
quota, unit by unit, until** the marginal revenue curve crosses
the marginal cost curve (in this case, supply curve). Output
will expand until **marginal revenue equals marginal cost. At
this output level the profit to egg producers will be maximized.**

If, starting from the output Q_{1} in Figure 6, the
Board were to increase the output quota by one more unit, the increase
in total revenue from selling that unit would be less than the
increase in the total cost from producing it, making such an
expansion of the quota not worthwhile. Alternatively, if it
were to reduce the quota by one unit, the reduction in total
revenue from selling one less unit would be greater than the
reduction in the total cost from producing one unit less, making
the reduction in the quota not worthwhile. Profits are maximized by
adjusting the quantity sold to equalize marginal cost and marginal revenue.

**Economists have a convention of referring to the elasticity
of demand as positive number even though it is in fact negative.**
When they talk about an elasticity of demand greater than 1 they
really mean that the elasticity of demand is less than -1. **What
they are referring to is the absolute value of the elasticity of
demand.** The absolute value of -2 is 2, whereas its algebraic
value is -2. We obtain a number's absolute value by simply
ignoring its sign. **So when economists say that the demand is highly
elastic they mean that the elasticity is a large number with a negative
sign attached.**

It is test-time again. Make sure that you think up an answer of your own before looking at the one provided.

Question 1

Question 2

Question 3

Choose Another Topic in the Lesson.