Question

The Organization for the Promotion of Brussels Sprouts has convinced the government of Ironia to institute a price floor on the sale of Brussels sprouts, at $8 per bushel. Demand is given by:

P = 9 – Q

and supply by:

P = 2Q,

where Q is measured in thousands of bushels.

Instructions: Round your answers to the nearest whole number.

a. At market equilibrium, the price is $________ per bushel, and the equilibrium quantity is_______ thousand bushels.

b. With the price floor, the price is $_________ per bushel, and the quantity sold is________ thousand bushels.

c. The excess supply of Brussels sprouts produced with the price floor is______ thousand bushels.

Answer 1

a)

Equilibrium is set at the point where, market demand is equal to the market supply.

Calculate the price and quantity demanded as follows:

\(9-Q=2 Q\)

\(9=2 Q+Q\)

\(9=3 Q\)

\(Q=3\) units

Thus, the equilibrium quantity demanded is 3units.

\(P=9-Q\)

\(=9-3\). \(=\$ 6\)

Thus, the equilibrium price is \(\$ 6\).

b)

Price floor is set above the market equilibrium. If it is set below, then shortage occurs.

With the price floor, the price is at \(\$ 8\).

Calculate the price and quantity sold with the price floor as follows:

\(P=9-Q\)

\(8=9-Q\)

\(Q=\) lunit

Thus, the quantity demanded at price ceiling is 1 lunit.

\(8=2 Q\)

\(Q=\frac{8}{2}=4\) units

Thus, the quantity supplied is 4 units

c)

calculate the excess supply as follows:

Excess supply = quantity supplied - quantity demanded \(=4-1\)

\(=3\) units

Thus, the excess supply is 3 units.