Question

suppose the quantity support for corn is:Qs=150 +14p and the deamand function for this corn is :P=16.875-0.0625Q with ten number of buyers and sellers ,were price is measured in dollars per bushels and quantities are in million of bushels per year.then
A,find the market equilibrium price and equilibrium quantity of corn
B,find the price elasticity of demand and supply at equilibrium price and quantity and interpret the result

Answer 1

a)Let's first rearrange our demand function:

$$0.0625Q=16.875-P,$$ $$Q_d=270-16P.$$

Let's find the equilibrium price and quantity. In the equilibrium, $Q_d=Q_s$ and we can find the equilibrium price:

$$270-16P_E =150+14P_E,$$ $$30P_E=120,$$ $$P_E=\$4.$$

Then, we can find the equilibrium quantity by substituting $P_E$ into the equation for $Q_d$:

$$Q_d=Q_s=Q_E=270-16\cdot4=206.$$

b) Let's rewrite our equations for $Q_d$ and $Q_s$ in slope-intercept form:

$$P=16.875-0.0625Q_d,$$ $$P=0.071Q_s-10.71.$$

The price elasticity of demand can be found as follows:

$$E_d=(\dfrac{-1}{slope})(\dfrac{P}{Q_d})=(\dfrac{-1}{(-0.0625)})(\dfrac{4}{206})=0.31$$

The price elasticity of supply can be found as follows:

$$E_s=(\dfrac{1}{slope})(\dfrac{P}{Q_s})=(\dfrac{1}{0.071})(\dfrac{4}{206})=0.27$$