Question

In: Economics

if the demand curve is Q(p)=p*, what is the elasticity of demand? if marginal cost is...

if the demand curve is Q(p)=p*, what is the elasticity of demand? if marginal cost is 1$ and *= -2, what is the profit maximizing price?

Expert Solution

Solution:

1)Given demand function Q(p) = P* where * represents -2

Q= P^(-2)

Which is Q = 1/ P ^ (2) where Q is a function of P.

For finding elasticity, let us assume that initial price P is $1 and the new price P is $2

This makes Initial quantity demanded set at 1 and Quantity demand after change in price at 1 / 4 or 0.25

We have seen that Percentage change in price is 100% and percentage change in quantity demanded is 75%

Price elasticity = percentage change in quantity demanded / percentage change in price

Price elasticity = 75 / 100 = 0.75

Therefore price elasticity is 0.75 ( absolute value only taken )

As price elasticity is 0.75 which lies in between 0 and 1 , then it is known that the demand is inelastic in nature as percentage change in quantity demanded is lesser than the percentage change in price.

Thus the demand is inelastic in nature.

2) Given function Q = 1/P ^2

When quantity is 1, total revenue is equal to marginal revenue as the addition towards revenue by selling 1 unit of the product is equal to the total revenue received by selling that 1 unit.

1 = 1 / P^2

P^2 = 1

Therefore P = $1

When price and quantity is 1 , the Total revenue = $1 ( P x Q )

At unit 1, TR =MR

Therefore , profit maximizing level condition is that MR = MC

At Price 1 , MR = 1 and MC = 1

Therefore the profit maximizing price is $1

Rahul Sunny answered 2 years ago

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