Training Economics Microeconomics — Supply, Demand & Elasticity
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Microeconomics — Supply, Demand & Elasticity

25 min Economics

Microeconomics studies how individuals and firms make decisions and how markets coordinate those decisions through prices. The core tool is supply-and-demand analysis: a demand curve shows the quantity consumers wish to buy at each price, and a supply curve shows the quantity producers wish to sell. Where they intersect — market equilibrium — determines the price and quantity that actually prevail. Elasticity measures how sensitively quantity responds to changes in price or income, allowing quantitative prediction of market outcomes when taxes, subsidies, or external shocks alter conditions.

Supply, Demand & Equilibrium

Law of Demand

Quantity demanded and price move in opposite directions, all else equal. A linear demand curve:

$$Q^d = a - bP, \quad b > 0$$

Law of Supply

Quantity supplied and price move in the same direction. A linear supply curve:

$$Q^s = c + dP, \quad d > 0$$

Market Equilibrium

Set $Q^d = Q^s$ and solve for the equilibrium price $P^*$ and quantity $Q^*$:

$$a - bP^* = c + dP^* \implies P^* = \frac{a-c}{b+d}, \quad Q^* = a - bP^*$$

Price Elasticity of Demand (PED)

$$E_d = \frac{\%\Delta Q^d}{\%\Delta P} = \frac{dQ}{dP} \cdot \frac{P}{Q}$$

$|E_d| > 1$ elastic; $|E_d| < 1$ inelastic; $|E_d| = 1$ unit elastic. Along a linear demand curve $Q = a - bP$: $E_d = -b \cdot P/Q$.

Consumer & Producer Surplus

With linear curves and equilibrium $(P^*, Q^*)$:

$$CS = \tfrac{1}{2}(P_{\max} - P^*)Q^*, \qquad PS = \tfrac{1}{2}(P^* - P_{\min})Q^*$$

Total surplus $= CS + PS$; a specific tax $t$ creates deadweight loss $DWL = \tfrac{1}{2}\,t\,|\Delta Q|$.

Tax Incidence Rule

A per-unit tax $t$ is split between buyers and sellers according to elasticity. Buyer's share of burden: $\frac{|E_s|}{|E_d|+|E_s|}\,t$. Sellers bear more of the tax when supply is more elastic than demand, and vice versa.

Example 1 — Equilibrium

Demand: $Q^d = 120 - 3P$. Supply: $Q^s = 2P - 30$. Find $P^*$ and $Q^*$.

  1. $120 - 3P = 2P - 30 \implies 150 = 5P \implies P^* = 30$, $Q^* = 120 - 90 = 30$.
Example 2 — Elasticity

At $P = 20$, $Q = 60$ on $Q^d = 120 - 3P$. Find PED.

  1. $E_d = (-3)(20/60) = -1$.
  2. Demand is unit elastic at this point.
Example 3 — Tax & DWL

A $\$5$ tax is imposed in Example 1. Find the new equilibrium, CS, PS, and DWL.

  1. Buyer pays $P_b$, seller receives $P_s = P_b - 5$.
  2. $120 - 3P_b = 2(P_b-5)-30 \implies 120-3P_b = 2P_b - 40 \implies P_b = 32$, $P_s = 27$, $Q = 24$.
  3. $DWL = \frac{1}{2}(5)(30-24) = \$15$.

Practice Problems

1. $Q^d = 100 - 2P$, $Q^s = 3P - 50$. Find equilibrium $(P^*, Q^*)$.
2. On $Q^d = 80 - 4P$ at $P = 10$, compute PED.
3. If PED $= -0.5$ and price rises $10\%$, what happens to quantity and total revenue?
4. Compute CS given $P^* = 20$, $P_{\max} = 50$, $Q^* = 40$.
5. A $\$4$ tax: $Q^d = 60 - P$, $Q^s = 2P - 30$. Find DWL.
6. Income elasticity of demand is $+2$ and income rises $5\%$. How much does $Q^d$ change?
7. Cross-price elasticity: goods with $E_{xy} > 0$ are ___; $E_{xy} < 0$ are ___.
8. Why does a price floor above equilibrium create a surplus?
9. Supply shifts right (increases). If demand is perfectly inelastic, what happens to $P^*$ and $Q^*$?
10. Compute PS given $P^* = 15$, $P_{\min} = 5$, $Q^* = 80$.
11. A $\$6$ specific tax on $Q^d = 50 - P$, $Q^s = P - 10$. How much do buyers pay? Sellers receive?
12. At what output does a firm with MR $= 20 - 2Q$ and MC $= 4$ maximize profit?
Show Answer Key

1. $100-2P=3P-50 \Rightarrow P^*=30$, $Q^*=40$.

2. $E_d = -4 \cdot 10/40 = -1$ (unit elastic).

3. $\%\Delta Q = -0.5 \times 10\% = -5\%$. TR rises (inelastic).

4. $CS = \frac{1}{2}(50-20)(40) = \$600$.

5. Equil: $P^*=30, Q^*=30$. With tax: $P_b=32, Q=28$. $DWL=\frac{1}{2}(4)(2)=\$4$.

6. $\%\Delta Q = 2 \times 5\% = +10\%$.

7. Substitutes; complements.

8. Price floor $>$ $P^*$ raises price above equilibrium, causing $Q^s > Q^d$ — surplus.

9. $P^*$ falls, $Q^*$ unchanged (perfectly inelastic demand).

10. $PS = \frac{1}{2}(15-5)(80) = \$400$.

11. Equil: $P^*=30, Q^*=20$. Tax: $P_b=32, P_s=26, Q=18$. Buyers pay $\$32$, sellers receive $\$26$.

12. $MR=MC \Rightarrow 20-2Q=4 \Rightarrow Q=8$.

Macroeconomics — GDP, Inflation & Unemployment