Question

Subject: Managerial Economics

Given the demand and supply equations for wheat Q^d = 40 - 3P and Q⁵ = 5 + 2P. Quantity is measured in bushels and price is in dollars per bushel. Answer the following questions:

4.1 What are equilibrium price and quantity?

4.2 Determine quantity demanded, quantity supplied and the dollar value of the surplus given a price floor of $9.

4.3 Determine quantity demanded, quantity supplied and the dollar value of the shortage given that there is a price ceiling of $5. Determine the full economic price paid by consumers.

Answer 1

Equilibrium at Qd=Qs

40-3P = 5+2P

5P = 35

P = 35/5 = 7

Q = 5+2*7 = 19

When price floor is $9, it is above the equilibrium price so will be binding.

Qd = 40-3*9 = 13, Qs = 5+2*9 = 23, Surplus = 23-13 = 10 units

Producer Surplus = (9-4)*13+(4+2.5)*0.5*13 = 107.25

Consumer Surplus = 0.5*(13.33-9)*13 = 28.145

A price cieling of $5 will be binding.

Qd = 40-3*5 = 25, Qs = 5+2*5 = 15 Shortage = 25-15 = 10 units

Producer Surplus = 0.5*7.5*15,

Consumer Surplus = 0.5*(13.33-8.66)*15+(8.33-5)*15 84.975 = 56.25