Elasticity of Demand: Consider the D function: Q=D(x)= 100-8x Where q is the qua

Question

Elasticity of Demand: Consider the D function:
Q=D(x)= 100-8x
Where q is the quantity of Christopher Ragle scarves demanded at a price of x dollars per scarf.
a. Find the elasticity Find the elasticity at x = $5.00 and state Whether the demand is elastic or inelastic. b. Find the elasticity at x = $8.88 and state whether The demand is elastic or inelastic C. At the price of $5.00 will a small increase in Price cause the total revenue to increase or decrease d. Find the value x for which the total revenue is Maximum? e.

Explanation / Answer

From the given question,

Q=D(x)= 100-8x

q=quantity

x=price

a)Elasticity= %change in quantity/%change in price

dQ/dx= -8

Elasticity=-(-8)(x/100-8x)

b)When x=$ 5

Elasticity of demand=-(-8)(5/100-8*5)

=2/3

As Elasticity of demand<1, the demand is inelastic.

c)When x=$ 8.88

Elasticity of demand=-(-8)(8.88/100-8*8.88)

=2.45

As Elasticity of demand>1, the demand is elastic.

d) Revenue (R)=(100-8x )(x)

=100x-8x2

dR/dx= 100-16x

at x=5, dR/dx=20,

small increase in price will cause revenue to increase.

e)for maximum revenue, dR/dx=0

100-16x=0

x=100/16

=6.25

Maximum revenue=100*6.25-8*(6.25)2

=$312.5

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