Question

Suppose that the demand equation for widgets is Qd=10,000−25P

What is the price elasticity of demand when P=$200?

What is the firm’s total revenue at P=$200?

What is the firm’s marginal revenue at P=$200?

What is the price elasticity of demand if the price of widgets falls to P=$150?

At P=$150, what is the firm’s total revenue?

At P=$150, what is the firm’s marginal revenue?

Answer 1

Answer
What is the price elasticity of demand when P=$200?
Price elasticity of demand=(dQ/dP)*(P/Q)
Q=10000-25*200=5000
dQ/dP=-25
E=(-25)*(200/5000)
=-1
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What is the firm’s total revenue at P=$200?
TR=P*Q=5000*200=1000000
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The inverse demand curve is
P=400-0.04Q
MR=400-0.08Q...........the MR curve is double sloped than demand curve.
MR=400-0.08*5000
=0
also, we do not need to calculate it, the elasticity is -1 so the revenue is maximum and the MR=0, we can conclude this theoretically.

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Q=10000-25*150=6250
E=(-25)*(150/6250)
=-0.6
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TR=6250*150=937500
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MR=400-0.08*6250=-100