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Price Elasticity of Demand Concepts

See the attached file.

1. Consider an inverse demand function p=40-q/5
(a) Find the price elasticity when price is $5.
(b) Find the price at which elasticity is -0.6.
(c) Suppose you are currently producing 125 units. If you raise your quantity a little bit, will your revenue increase or decrease? Using elasticity concept, explain your answer.

2. Consider an inverse demand function p=500-q/20.
(a) Find the price at which the elasticity is -0.4.
(b) Find the quantity, q*, and price, p*, that maximize the revenue.
(c) Suppose you have a capacity constraint that limits your maximum production to 4,000 units. What is the price and quantity that maximize your revenue. Call the price p** and quantity q**.
(d) Find the price elasticity at p**.

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See the attached file.

1. a) p=40-q/5
On rearranging, we get
q/5=40-p
q=200-5p
Differentiate with respect to p, we get
dq/dp=-5
q at p=$5, is given by
q=200-5*5=175
Price elasticity of demand at p=$5 is given by
Ep=(dq/dp)*(p/q)=-5*(5/175)= -0.14286

b) p=40-q/5
On rearranging, we get
q/5=40-p
q=200-5p
Differentiate with respect to p, we get
dq/dp=-5
Price elasticity of ...

Solution Summary

There are two problems. Solution to these problems explain the methodology to calculate price elasticity of demand at given price, price at given value of price elasticity and revenue maximizing price.

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