Answer to Question #106241 in Microeconomics for Mi

Question

(A) the inverse demand functions of two towns for a product are given as (Q1/2)1/4=P and {2-Q2/10}=P. find the market demand of these two towns.

(B) 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

a)(Q1/2)1/4 = P and 2 - Q2/10 = P The market demand of these two towns is the sum of individual demands, so:

$2P = Q1/8 - Q2/10 + 2,$

$P = Q1/16 - Q2/20 + 1.$

b) Qs =100 and Qd =50p - 1/2 + 10.

i) the equilibrium price and quantity are:

Qd = Qs,

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

$50p = 90.5,$

p = 1.81,

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 from current price of 80 pesewas 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 Ghs 0.6 is imposed on the producer, then the equilibrium price will increase, and the equilibrium quantity will decrease.