Answer to Question #323998 in Microeconomics for Yonatan

Question

Given the following Demand and supply function: Q_{d = 12 - P} and Q_{s = 8.4 + 0.5P} , 

then answer the following questions.  

i. Calculate the market clearing price and quantity. 

ii. Determine, whether surplus or shortage exist at price level of 2 birr and 3 Birr. 

iii. Compute price elasticity of demand and supply at equilibrium level of price and 

quantity 

iv. Determine the nature of price elasticity of demand and supply and interpret the result.  

Answer 1

i. $12-P=8.4+0.5P$

$1.5P=3.6$

$P=2.4$

$Q=9.6$

ii. At a price level of 2 birr:

$Q_d=12-2=10$

$Q_S=8.4+1=9.4$

It's shortage.

At a price level of 3 birr:

$Q_d=12-3=9$

$Q_S=8.4+1.5=9.9$

It's surplus.

iii.$E=\frac{\Delta Q/Q}{\Delta P/P}$

$E_d=\frac{0.4/9.6}{-0.4/2.4}=-0.25$

$E_S=\frac{-0.2/9.6}{-0.4/2.4}=0.125$

iv. Negative price elasticity of demand means that the quantity demanded falls when the price rises.

The price elasticity of supply is positive, so the supply rises with price growth. Since the price elasticity of supply is less than 1, the supply is inelastic (low responsive to price changes).