Question

Keiko has quasilinear preferences. Her demand for toothpaste is q(p) = 10 ? p and her inverse demand is p(q) = 20 ? 2q. If Keiko were the only consumer in the market, what price maximizes revenue?

Answer is 10

What is the elasticity of Keiko’s demand at p = 8?

Answer is - 2/3 inelastic

Could you show me the steps to solve the problem? Thank you!

Answer 1

Answer
the given main demand function is not correct, the only the inverse demand curve is correct as per your answers

the revenue is maximum when the MR=0
MR=20-4q .......... the MR curve is double sloped than the demand curve
equating to zero
20-4q=0
4q=20
q=5
P=20-2*5=10
the revenue is maximum at P=$10
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the demand function is
p=20-2q
p+2q=20
2q=20-p
q=10-0.5p

elasticity of demand =(dq/dp)*(p/q)
dq/dp=-0.5
q=10-p=10-0.5*8=6
elasticity of demand =(-0.5)*(8/6)=(-2/3)
the demand elasticity is (-2/3) and it is inelastic because the elasticity is above -1.

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