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This is Elasticity, revenue and who bears a tax.

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This walkthrough uses a generic synthetic narrator, not a
recording of Craig Wright.

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Pause whenever you need time to calculate.

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The original lesson, written walkthrough and exercises
accompany this video.

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Percentage changes make responses comparable.

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If a quantity rises from 50 to 55, the change is five units and
the starting-base percentage increase is

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five divided by 50, or ten per cent.

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If an interest rate rises from four per cent to five per cent,
it rises by one percentage point but by 25

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per cent relative to its initial value.

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These are different measures.

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Elasticity uses proportional changes, allowing comparisons
across units such as boxes, kilograms or litres.

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Always identify the relevant base and sign before calculating.

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A calculator cannot correct an ambiguous definition of the
percentage you intend to measure.

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Demand elasticity is a conditional response.

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An elasticity of minus two means that, locally, a one per cent
price increase is associated with about a two

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per cent reduction in quantity demanded, other relevant
conditions unchanged.

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The absolute magnitude is two.

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Be explicit about whether you report the signed value or its
magnitude.

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Elastic does not mean that quantity is high; it means quantity
responds proportionally more than price.

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An inelastic response is not necessarily zero.

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Perfectly inelastic demand has zero quantity response in the
specified model and range, a much stronger

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condition than merely having a magnitude below one.

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Worked example: use the midpoint method.

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Step one calculates the changes: price increases by two pounds
and quantity decreases by twenty units.

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Step two calculates the average of each pair of endpoints:
eleven pounds and ninety units.

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Step three divides each change by its own average, giving
approximately 0.1818 and negative 0.2222.

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Step four divides the quantity proportion by the price
proportion.

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The result is negative eleven-ninths, or approximately negative
1.222.

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Using midpoint bases gives the same magnitude when the
direction of comparison is reversed.

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Do not divide a percentage quantity change by a raw pound
change; that would not be an elasticity.

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Revenue connects price and quantity.

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Calculate revenue independently to check the interpretation:
ten pounds times one hundred is one thousand

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pounds; twelve times eighty is nine hundred and sixty.

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Revenue falls by forty pounds.

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For positive endpoints, the midpoint elasticity classification
is consistent with this finite-change revenue

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test.

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If its magnitude is exactly one, the two endpoint revenues are
equal.

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The relationship assumes the observed quantity change is a
movement along unchanged demand and that all

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units sell at the stated price.

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Revenue is not profit.

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Costs, returns, discounts and capacity constraints may change
whether a pricing decision benefits the

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seller.

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Worked example: an inelastic price cut.

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First take the signed changes: quantity rises by four and price
falls by two.

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Divide by the midpoint bases to get about positive 7.692 per
cent and negative 10.526 per cent.

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Dividing those proportions gives negative
nineteen-twenty-sixths, approximately negative 0.731.

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Its magnitude is below one, so demand over this interval is
inelastic.

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Next calculate revenues: 20 times 50 equals 1,000, while 18
times 54 equals 972.

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The price cut reduces revenue by 28 pounds.

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More customers or more units sold therefore does not
necessarily imply more sales revenue, still less more

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profit.

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A straight line can have changing elasticity.

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The same ten-unit response is a larger percentage of a small
starting quantity than of a large one.

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Likewise, a one-pound change is a smaller percentage of a high
price than of a low price.

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That is why a constant slope need not imply constant
elasticity.

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The point formula multiplies the quantity response per pound by
price divided by quantity.

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At five pounds, it gives negative ten times five divided by
150.

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At fifteen pounds, it gives negative ten times fifteen divided
by fifty.

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Point elasticity describes a small local change; midpoint
elasticity summarises an interval between two

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distinct observations.

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Substitution and time influence responsiveness.

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A particular café may have many nearby substitutes, while
coffee as a broad category has fewer close

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alternatives for some customers.

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Buyers may respond to a lasting fuel-price change by changing
routes, vehicles or housing, even if

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tomorrow's commute barely changes.

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The relevant time horizon therefore matters.

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Different groups can also have different responses.

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An average market elasticity can conceal people who have few
short-run alternatives.

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To use an estimate responsibly, check its product definition,
population, period, price range and research

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design.

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An elasticity borrowed from a different setting may be a poor
guide.

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Supply has an elasticity too.

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A bakery with unused ovens may increase output quickly, while a
fully booked venue cannot create more seats

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for tonight merely because offers rise.

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Over a longer period, investment or entry can make supply more
responsive.

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These examples concern conditional responses, not shifts caused
by new technology or input-price changes.

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As with demand, distinguish a local elasticity from an estimate
over a large interval.

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A vertical supply curve means fixed quantity in the model's
relevant range, whereas a horizontal curve

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represents an extremely responsive supply at the given price.

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Neither shape is appropriate for every market.

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Other elasticities answer other questions.

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Do not interpret all elasticities as own-price demand
elasticity.

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If bus fares rise and train demand increases, the cross-price
response can indicate substitution between

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travel options.

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If printer prices rise and demand for ink falls, the goods may
be complements.

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These labels depend on the context and level of aggregation;
they are not timeless characteristics of every

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individual's preferences.

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Income elasticity also varies across groups and income ranges.

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The word inferior has no moral meaning here.

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As always, an observed correlation is not automatically a
causal response when incomes, prices and other

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conditions move together.

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A tax introduces a price wedge.

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Before introducing the tax, set buyer and seller prices equal
to P.

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Equilibrium is 100 minus 2P equals 10 plus P, giving 90 equals
3P and P equals 30.

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Supply then gives 40 units.

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With the tax, using a single price in both original schedules
would erase the distinction we need to

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analyse.

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Buyers respond to the amount they pay, while sellers respond to
what they retain per unit after the tax.

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We assume a competitive market, compliance, unchanged
underlying schedules and no separate administrative

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costs or other policy effects.

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Worked example: calculate tax incidence.

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Expand the left side carefully: 100 minus 2Ps minus 12 equals
10 plus Ps.

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Subtract ten and collect price terms to obtain 78 equals 3Ps.

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Dividing by three gives 26, then adding the six-pound tax gives
the buyer price of 32.

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Check quantities: demand is 100 minus 64, or 36; supply is 10
plus 26, also 36.

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Tax revenue is six times 36, or 216 pounds.

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The buyer and seller burdens per traded unit sum to the tax:
two plus four equals six.

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This is a particular model calculation, not a general
two-to-one incidence rule.

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Legal payment and economic burden can differ.

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Use the local elasticity formulas at the original price of 30
and quantity of 40.

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Supply's slope is one, so its elasticity is one times 30
divided by 40, or 0.75.

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Demand's slope is negative two, giving magnitude two times 30
divided by 40, or 1.5.

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Sellers are less responsive in this example.

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This intuition concerns relative ability to adjust quantities.

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Market power, evasion, price regulation, cross-border options
and longer-run changes can alter the result.

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A positive incidence calculation also does not decide whether a
tax is justified; that judgement needs

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stated goals, rights and other consequences.

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A correlation is not a demand experiment.

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Imagine comparing a quiet rainy Tuesday with a crowded sunny
Saturday.

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Weather, visitors, opening hours and stock could differ
alongside price.

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Dividing the observed percentage quantity change by the
observed price change gives a descriptive ratio, but

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not necessarily demand elasticity.

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A controlled comparison might hold other conditions more nearly
constant, while a research design may use a

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source of price variation unrelated to demand changes.

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Neither method is automatically flawless.

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Check selection, spillovers, measurement, compliance and the
range of prices studied.

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Report uncertainty rather than presenting a single estimate as
a universal behavioural constant.

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Calculate, interpret, then qualify.

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A reliable answer has three layers.

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First comes arithmetic: changes, averages, ratios and units.

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Second comes interpretation: what the magnitude means for the
specified demand or supply relationship.

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Third comes identification and scope: why the data support a
causal statement and where the estimate might

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fail to transfer.

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The exercises deliberately include a case where arithmetic is
possible but a causal demand interpretation is

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not established.

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Written reflections remain ungraded.

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Use them to explain assumptions and evidence, because checking
a number cannot substitute for understanding

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the model or the way the observations were generated.