Question

4. (6 points) Suppose the Demand for baseballs is given by Q = 120 – 4P. a) What is the price elasticity of demand when P= 10? b) At what price will Total Revenue be maximized? c) What is the firm's Marginal Revenue when the price is $12?

Answer 1

Answer

a)

the formula is:

$E=\frac{\partial Q}{\partial P}*\frac{P}{Q}\\ \frac{\partial Q}{\partial P}=\frac{\partial \left ( 120-4P \right )}{\partial P}=-4\\ P=10\ then\ Q=120-4*10=80\\ E=-4*\frac{10}{80}=-0.5$

the elasticity is -0.5

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b)

Converting the demand curve to the inverse demand curve

Q=120-4P

4P=120-Q

P=30-0.25Q

MR=30-0.5 Q ................ An MR curve is double sloped than an inverse linear demand curve

the total revenue is maximum when the MR=0

30-0.5Q=0

0.5Q=30

Q=60 units

P=30-0.25*60

P=$15

the revenue is maximum at P=15 and Q=60

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c)

Q=120-4P

P=12 then Q=120-4*12=72

MR=30-0.5Q=30-0.5*72=-6

the MR is -$12