Question

Having a hard time understanding the concept of Elasticity, If you can please be detailed.

QD = 1,600 – 125 * P
QS = 440 + 165 * P
You should have calculated the equilibrium in this market to be (P*, Q*) = ($4,
1,100).
a. Calculate the price elasticity of demand at the equilibrium. Is this elastic or
inelastic?
b. Calculate the price elasticity of supply at the equilibrium. Is this elastic or
inelastic?
c. Suppose the government sets a price floor of $4.50 in this market. What is the
quantity supplied at that price? What is the quantity demanded? Is this a
shortage or a surplus? How large is it?
d. Illustrate this graphically.

Answer 1

equilibrium is at Qd=Qs
equating both equations
1600-125P=440+165P
290P=1160
P=4
Q=1600-125*4=1100
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a)
price elasticity of demand =(dQ/dP)*(P/Q)
dQ/dP=-125 ......... the first derivate of the demand curve
price elasticity of demand =(-125)*(4/1100)
=-0.45454545454
=-0.45
The demand is inelastic as the elasticity of demand is above -1.

b)
price elasticity of supply =(dQ/dP)*(P/Q)
dQ/dP=165 ...... first derivative of the supply curve
price elasticity of supply=(165)*(4/1100)
=0.6
the supply is inelastic as the supply elasticity is below 1

c)
the price floor is above the equilibrium price, so it is binding.

What is the quantity supplied at that price?
Qs=440+165*4.5
=1182.5
quantity supplied is 1182.5 units

What is the quantity demanded?
Qd=1600-125*4.5
=1037.5
the quantity demanded is 1037.5 units

Is this a shortage or a surplus?

there is surplus as the Qs>Qd

How large is it?

Surplus =Qs-Qd
=1182.5-1037.5
=145
the surplus is 145 units

d)