Microeconomics: supply, demand, elasticity

The first semester started a little over a week ago. If you are a first-year Economics student, your Microeconomics course is opening right now with the longest block of the programme: supply and demand, which usually takes September and October before moving on to costs and indifference curves. Where the course has a mid-term test, it falls between late October and November; the exam on the whole block comes in the winter session. Check the exact dates on your course website, because every university has its own calendar. The real point is not when: it is that this block is built on reading graphs and using straight lines, and if you do not take five minutes to sort that part out now, you will drag it along until the exam.

What the exam really asks

The first block of Microeconomics revolves around demand and supply curves, market equilibrium, elasticity and, shortly after, consumer and producer surplus. Indifference curves and consumer theory come right after, and production costs later still. Here I concentrate only on the first block, the one that is starting in these weeks.

In my experience, the point where most marks are lost is not the calculation: it is reading and interpreting the graphs. Students who come from a non-scientific high school often have a weaker maths base on straight lines and slopes, and here that base is really needed. It is not for complicated calculations, but for reading a graph correctly before you even touch the numbers.

The convention that confuses everyone at first

In maths, if you write $y = f (x)$ , the vertical axis is the dependent variable. In microeconomics the convention is reversed: the vertical axis holds the price $P$ , which in everyday language we usually treat as the independent variable (“the price determines the quantity”), but the graph draws it as if it were the $y$ -axis. When you write the demand function as

Q_{d} = a - b P

that is the “direct” form: quantity as a function of price. To draw it with $P$ on the vertical axis, as is always done in microeconomics, you first have to invert it:

P = \frac{a - Q _{d}}{b}

If you do not make this step mentally every time, you risk reading a steeper line as “more elastic” when the opposite is true, or getting the direction of a shift wrong. It is the first hurdle of the course, and it is worth clearing it properly before going on. If you need to revise straight lines and slopes, you will find the method on the maths page.

Moving along the curve or shifting the curve: the distinction that matters most

A change in the price of the good itself produces a movement along the demand (or supply) curve: the curve stays still, only the point on it changes. A change in another factor shifts the whole curve. For demand these factors are income, prices of related goods (substitutes or complements), tastes, expectations, and the number of consumers. For supply they are the cost of inputs, technology, the number of producers and expectations.

Confusing the two is the most common conceptual mistake in this block: “the price went up, so demand fell” is almost always the wrong description of a movement along the curve (a change in the quantity demanded), not of a shift in demand. The words “demand fell” should be reserved for a true shift of the curve, caused by something other than the price of the good.

Equilibrium: where the two curves meet

Market equilibrium is the point where quantity demanded and quantity supplied coincide. You find it algebraically by setting $Q_{d} (P) = Q_{s} (P)$ and solving for $P^{*}$ , or graphically by looking for the intersection of the two curves. It is a single number, not an approximation: you will see it in the first exercise below.

Elasticity: it is not the slope

The price elasticity of demand measures by what percentage the quantity demanded changes when the price changes by 1%:

E_{d} = \frac{% Δ Q _{d}}{% Δ P} = \frac{d Q _{d}}{d P} \cdot \frac{P}{Q _{d}}

The first factor, $d Q_{d} / d P$ , is the slope of the function (in the direct form $Q_{d} = a - b P$ it is simply $- b$ , constant along the whole curve). The second factor, $P / Q_{d}$ , changes from point to point along the same line. That is why a demand line has a constant slope but a different elasticity at each of its points: near the vertical axis (high price, low quantity) the elasticity is high in absolute value, near the horizontal axis it is low. It is not enough to look at how “tilted” a curve is to say whether it is elastic: you have to calculate it at the specific point.

Three thresholds to keep in mind, always in absolute value:

$∣ E_{d} ∣ > 1$ : elastic demand (the quantity reacts more than proportionally to the price)
$∣ E_{d} ∣ = 1$ : unit elasticity
$∣ E_{d} ∣ < 1$ : inelastic demand (the quantity reacts less than proportionally)

The relationship with total spending ( $P \times Q$ ) is what makes elasticity useful and not just an abstract number. If demand is elastic, a price increase reduces total spending (the quantity falls by more than the price rises). If it is inelastic, a price increase raises total spending. This is the reasoning behind why a producer of a good with inelastic demand has an incentive to raise the price, and one with elastic demand does not.

Two variants that the course introduces right afterwards, in brief: cross-price elasticity measures how the quantity demanded of one good changes when the price of another good changes (positive for substitutes, negative for complements); income elasticity measures the same thing with respect to the consumer’s income (positive for normal goods, negative for inferior goods).

Four worked exercises

1. Equilibrium from two linear functions

A market has demand $Q_{d} = 120 - 2 P$ and supply $Q_{s} = - 30 + 4 P$ (price and quantity in any units, consistent with each other). Find the equilibrium price and quantity.

I set $Q_{d} = Q_{s}$ :

120 - 2 P = - 30 + 4 P ⟹ 150 = 6 P ⟹ P^{*} = 25

Substituting into one of the two functions:

Q^{*} = 120 - 2 \cdot 25 = 70

Check with the other: $Q_{s} = - 30 + 4 \cdot 25 = 70$ . They match, so the equilibrium is $(P^{*}, Q^{*}) = (25, 70)$ .

2. A demand shift and the new equilibrium

An increase in consumers’ income shifts the demand of the previous exercise to $Q_{d}^{'} = 150 - 2 P$ (at the same price, more is demanded: the curve has shifted to the right). Supply stays $Q_{s} = - 30 + 4 P$ . Find the new equilibrium.

150 - 2 P = - 30 + 4 P ⟹ 180 = 6 P ⟹ P^{**} = 30 Q^{**} = 150 - 2 \cdot 30 = 90

Both the equilibrium price and quantity have increased. This is the typical signature of a rightward shift of demand, unlike a movement along the curve, where price and quantity would move in opposite directions.

3. Point elasticity at the equilibrium point

In the market of exercise 1, calculate the price elasticity of demand at the equilibrium point and say whether demand is elastic or inelastic there.

From the function $Q_{d} = 120 - 2 P$ , the derivative is constant: $d Q_{d} / d P = - 2$ . At the equilibrium point $P^{*} = 25$ , $Q^{*} = 70$ :

E_{d} = - 2 \cdot \frac{25}{70} \approx - 0.71

$∣ E_{d} ∣ \approx 0.71 < 1$ : at this point demand is inelastic. Practical consequence: a small price increase around this equilibrium would make consumers’ total spending rise, because the quantity would fall by less than proportionally.

4. A per-unit tax: new equilibrium and deadweight loss

In the same market as exercise 1 ( $Q_{d} = 120 - 2 P$ , $Q_{s} = - 30 + 4 P$ , initial equilibrium $P^{*} = 25$ , $Q^{*} = 70$ ), the government introduces a tax of $t = 6$ per unit sold, paid by the producer. Letting $P$ be the price paid by the consumer, the producer receives $P - t$ : the equilibrium condition becomes $Q_{d} (P) = Q_{s} (P - t)$ .

120 - 2 P = - 30 + 4 (P - t) ⟹ 120 - 2 P = - 30 + 4 P - 4 t ⟹ 150 + 4 t = 6 P

With $t = 6$ :

P_{1} = \frac{150 + 24}{6} = 29

The consumer pays $29$ , the producer receives $P_{1} - t = 23$ , and the quantity traded falls to $Q_{1} = 120 - 2 \cdot 29 = 62$ (check: $- 30 + 4 \cdot 23 = 62$ , they match).

The deadweight loss is the area of the triangle between the two curves, between the old and the new quantity:

D W L = \frac{1}{2} \cdot t \cdot (Q^{*} - Q_{1}) = \frac{1}{2} \cdot 6 \cdot (70 - 62) = 24

Tax revenue, on the other hand, is $t \cdot Q_{1} = 6 \cdot 62 = 372$ . It is not deadweight loss: it is value that moves from private parties to the public purse. The deadweight loss is only the part of surplus that disappears altogether, because those 8 units of trade (between $Q_{1} = 62$ and $Q^{*} = 70$ ) no longer take place.

Typical mistakes

Mixing up movement along the curve and a shift of the curve. This is the number one conceptual mistake, described above. Before answering a question about “what happens to the market”, ask yourself whether the cause is the price of the good itself (movement along the curve) or something else (a shift).

Forgetting to invert the function to read it on the graph. Demand in the form $Q_{d} = a - b P$ and its version $P = (a - Q_{d}) / b$ are the same line, but if the question asks for the intercept on the price axis and you look at the intercept of the direct form, you get the wrong number.

Confusing slope and elasticity. A line has a constant slope but an elasticity that changes along its whole length. You cannot say “it is an elastic curve” without specifying at which point.

Adding the tax to the old equilibrium price instead of recalculating the equilibrium. The tax is not added to the price that was there before: it changes the equilibrium conditions, and the new price paid by the consumer generally rises by less than the whole tax (in the exercise above, the tax is 6 but the price paid rises by only 4, from 25 to 29; the producer absorbs the difference).

How we work in lessons

On this block I always start from the graph drawn by hand, before any calculation: axes with the right labels, curves with the right slope, arrows for the shifts. The vast majority of mistakes I see, even in students who are good at algebra, come from a graph read or drawn badly, not from a wrong calculation. Once the graph is solid, the calculations (equilibrium, elasticity, surplus) become almost mechanical.

If you come from a non-scientific high school and the maths of the course seems a bigger obstacle than the economics itself, you are not an isolated case. The problem is almost always confidence with straight lines and slopes, not the economics, and it can be fixed in a few targeted lessons. You will find the overall picture on the page for university tutoring; to fix the basics of straight lines and slopes, see the maths page.

There is not yet a dedicated exam practice test for Microeconomics, but you will find several practice tests for first-year exams in the university practice tests section, useful for training in the meantime on other subjects of the semester.

If you come from an economics technical school (istituto tecnico economico), the basic vocabulary is in double-entry bookkeeping and in first-year law.

If you would like a hand setting up this block properly before the mid-term test, write to me through the contact page: tell me where you are with the course exercises and I will honestly tell you where it makes sense to start.

Microeconomics: supply, demand and elasticity