Find the incidence of a $50 per unit tax imposed by law on the supplier.

Question

The demand for a good is XD = 2500-3P and the supply is XS=7P where X is the number of units and P is the price per unit. In equilibrium without taxes the price is 250 and the quantity of X that is traded is 1750.

A) Find the incidence of a $50 per unit tax imposed by law on the supplier. Be sure to explain what is meant by incidence and how you are measuring it.

Answer 1

1. Pre-Tax Equilibrium:

We are given that the demand function is:

X_D = 2500 − 3P

And the supply function is:

X_S = 7P

The pre-tax equilibrium occurs where X_D = X_S​. Setting the two equations equal:

2500 − 3P = 7P

Solving for P:

P = 250

At a price of P = 250, the quantity traded is:

X= 7P = 7(250) = 1750 units.

2. Impact of a $50 Tax on the Supplier:

With a tax of $50 per unit on the supplier, the supply curve shifts upward by $50. This means that for every price P, the supplier now receives P − 50. Therefore, the new supply equation becomes:

X_S = 7(P − 50) = 7P − 350

The new equilibrium occurs where demand equals the new supply:

2500 − 3P = 7P − 350

P = 285

So the new equilibrium price paid by buyers is $285.

3. Quantity Traded After the Tax:

To find the new quantity traded at this price, substitute P = 285 into either the demand or the supply function:

X_D = 2500 − 3(285) = 1645 units

4. Price Received by Sellers:

Since the price buyers pay is $285, and the tax is $50, the price that sellers receive is:

P_seller = 285 − 50 = 235

5. Tax Incidence:

Buyer's burden: The price paid by buyers increased from $250 to $285, so the buyer's tax burden is:

285 − 250 = $35 per unit.

Seller's burden: The price received by sellers fell from $250 to $235, so the seller's tax burden is:

250 − 235 = $15 per unit.

Thus, the incidence of the $50 tax is:

Buyers bear $35 of the tax.

Sellers bear $15 of the tax.

The incidence of the tax shows that the buyers bear a larger share of the tax burden ($35) compared to the sellers ($15). This distribution of the tax burden depends on the relative price elasticity of supply and demand. Since the buyers' price increased more than the decrease in the price received by sellers, we can infer that demand is relatively inelastic compared to supply.