Answer to Question #106240 in Microeconomics for Dede

Question #106240
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?
1
Expert's answer
2020-03-30T07:24:26-0400

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\u00d7(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.


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