Suppose market demand and supply are given in a perfectly competitive market for

Question

Suppose market demand and supply are given in a perfectly competitive market for bushels of wheat by:

Determine the equilibrium price and quantity. Show the equilibrium graphically. (Quantity can be in fractions of a bushel.)

Suppose a $30 excise tax (tax on each unit sold) is imposed on the good. Determine the new equilibrium producer price, consumer price, and quantity. Indicate these items graphically. How much of the tax do the consumers pay per unit? (What is their tax burden?). How much of the tax do the producers pay per unit? (What is their tax burden?)

With the $30 tax in place, what are the consumer surplus, producer surplus, government revenue, and deadweight loss? Indicate these items graphically.

Explanation / Answer

To find equilibrium price and quantity,

equate supply and demand functions,

500-5q=400+10q

q=6.6

p=466

With the imposition of a $30.00 tax per unit, the price buyers pay is $30 more than the

price suppliers receive. Also, at the new equilibrium, the quantity bought must equal

the quantity supplied. We can write these two conditions as

Pb – Ps = 30

Qb = Qs.

Let Q with no subscript stand for the common value of Qb and Qs. Then substitute the

demand and supply equations for the two values of P:

(500-5q) – (400+10q) = 30

q=4.6

plug in demand equation, we get Pb=477,

Ps=446

deadweight loss=tax per unit x new quantity

=30x4.6

=138

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