Question

Suppose the demand and supply equations for wheat per year in a country can be specified as follows ? : Q (D) = 500 – 2P Q(S) = – 100 + 4P P is the price in dollars per thousand bushels and Q is the quantity of wheat in thousands of bushels.

a) How to solve for the equilibrium price and quantities traded and illustrate your answer with a diagram ?
b) How to compute and show on your diagram the vertical intercepts for both the demand and supply curves and the horizontal intercept for the demand curve ?

Answer 1

Equilibrium price `p=33.3`
Equilibrium quantity `q=33.4`

Explanation:

Given -

`Q_d=100-2p` Demand Function
`Q_s=-100+4p` Supply Function

Equilibrium price and quantity are determined by equating demand and supply.

`100-2p=-100+4p`
`-2p-4p=-100-100`
`-6p=-200`
`p=(-200)/(-6)=33.3`

Equilibrium price `p=33.3`

To get equilibrium quantity substitute `p=33.3` either in the demand or supply function

`Q_d=100-(2xx33.3)`
`Q_d=100-66.6=33.4`

Equilibrium quantity `q=33.4`

The vertical and horizontal intercepts are show in the diagram.