Consider the following market for good x (finely divisible). Q = 2 P; and ; Q=16/√P; * Identify the demand and the supply functions * Find the equilibrium price and quantity * What would happen (Surplus or shortage) if this market was imposed: A price of 5 dollars per unit? * Calculate the elasticity of demand at the price P= 8. (Elastic or Inelastic? Why?)

Consider the following market for good x (finely divisible).
Q = 2 P; and ; Q=16/√P;

* Identify the demand and the supply functions
* Find the equilibrium price and quantity
* What would happen (Surplus or shortage) if this market was imposed: A price of 5 dollars per unit?
* Calculate the elasticity of demand at the price P= 8. (Elastic or Inelastic? Why?)

 

 

Answer:

The demand function is Q=16/√P

The supply function is Q = 2 P

At Equilibrium demand equals supply

2P=16/√P

P√P=8

P=8(1.5)

P=22.6

Q=2*22.6= 45.2

At a price of $5 there would be a shortage.

Ep=dQ/dP * (P/Q)

Q=16/√P

When P=8 , Q=5.65

dQ/dP=-8/P1.5

Ep=(-8/P1.5)* (P/Q)

Ep=-0.5

Inelastic, since the elasticty is less than 1.

Asked on February 14, 2018 in economics.
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