The market for pumpkins is a competitive market where the quantity of crates dem

Question

The market for pumpkins is a competitive market where the quantity of crates demanded is given by Qd = 18.2 – 0.2P and the quantity of crates supplied is given by Qs = (P/6) – 0.5.

Provide the inverse demand and inverse supply functions for pumpkins. What is the equilibrium price and quantity in this market?

A tax of $44 per crate of pumpkins is imposed on thepumpkin sellers. What is the equilibrium price and quantity after the tax? How much tax revenue and how much deadweight loss are produced by the tax onpumpkins?

Explanation / Answer

1. Inverse demand for pumpkin is: P=1/0.2(18.2-Qd)

and inverse supply for pumpkin is: P=6(Qs+0.5)

2. At equilibrium Qd=Qs

So, 18.2-0.2P=P/6-0.5

Thus, P=187/62=3.01

Thus, Q=18.2-0.2x3.01=17.39

3. After tax of $44 equilibrium will be at:

18.2-0.2 P=(P+44)/6-0.5

or, P=4.19

Hence, Q=18.2-0.2x4.19=17.36

4. Deadweight loss=0.5x(4.19-3.01)x(17.39-17.36)=0.017

Tax revene=$44x17.36=$763.84

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