Question

Use the equations below to answer the following questions

P=60-1/3Qd

2p=40+2/5Qs

Calculate the equilibrium price and quantity

If the is set at p=40,state whether it is a price ceiling or price floor and calculate the size of imbalance

Calculate the price elasticity of demand and supply

Answer 1

Equilibrium Price and Quantity.

$P=60-\frac{1}{3}Q_d$

$Q_d=180-3P$

$2P=40+\frac{2}{5}Q_s$

$Q_s=5P-100$

at equilibrium, $Q_d=Q_s$

$\therefore 180-3P=5P-100$

$280=8P$

$\bold{P=35}$

Replacing the value of P in either the $Q_d$ or $Q_S$ we get the value of quantity as;

$180-3(35)=75$

$\bold{Q=75}$

When the price is set at $P=40$ , it is to be considered as a price ceiling. Since the price ceiling is above the equilibrium price, then there is no imbalances arising in the market.

Price Elasticity(Ped)

$Ped=\frac{\delta Q/Q}{\delta P/P}$

at $P=40,$ $Q=180-3(40)=60$

$\delta Q=60-75=-15$

$\delta P= 40-35=5$

$Ped=\frac{-15/60}{5/40}=-2$

$\bold{Ped=-2}$