Effect of a tax

Introducing a tax shifts the supply curve and changes the equilibrium point: the model lets us compute how the tax burden is shared between consumers and producers.

Example — Effect of a tax

A tax of $4$ EUR/q is introduced, payable by the producers. The supply curve shifts: to supply the same quantity the producer wants a gross price higher by $4$: $Q_s^{\text{nuovo}}(p) = -40 + 3(p-4) = -52 + 3\,p.$ New equilibrium: $200-5p=-52+3p\Rightarrow p^{\ast\ast}=31{,}5$, $Q^{\ast\ast}=42{,}5$.

• Consumers pay $1{,}5$ EUR/q more ($30\to 31{,}5$): they have borne $\tfrac{1{,}5}{4}=37{,}5\%$ of the tax.
• Producers collect $31{,}5-4=27{,}5$ EUR/q ($30\to 27{,}5$): they bear the remaining $62{,}5\%$.

The tax burden is shared according to the elasticities of the two curves: the more rigid (less elastic) a curve is, the more tax ends up borne by whoever is on that side (Varian). The concept of elasticity as a “logarithmic derivative” we will revisit when studying exponential and logarithmic functions.

Links

Topics: Linear systems
Concepts: Supply and demand · Elasticity · Equilibrium price
Skills: Model · Solve systems