Question

the supply and demand functions for a product are defined as Q =100 and Qd =50P^ -1/2+ 10

i)find the equilibrium price and quantity

ii)sketch a graph to show the results in i)above

iii)Assume the equilibrium price is 80 cents (p=0.80)find the PES and PED associated with a small increase in price from current price of 80 cents

iv)What is the incidence of a tax of $0.6 imposed on the producer?

Answer 1

i) the equilibrium price and quantity are:

Qd = Qs,

$50p^{-1/2} + 10 = 100,$

$50/p^{1/2} = 90,$

$p^{1/2} = 5/9,$

$p = 25/81 = 0.3,$

Q = 100 units.

ii) the equilibrium price and quantity can be shown as intersection point of supply and demand curves.

iii) If the equilibrium price is p = 0.80, then PES and PED associated with a small increase in price are:

PES = infinity, because the supply is perfectly elastic.

$PED = -50×(0.8/100) = -0.4,$

so the demand is inelastic.

iv) If a tax of 0.6 is imposed on the producer, then the equilibrium price will increase, and the equilibrium quantity will decrease.