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For the demand function q equals Upper D (p )equals 357 minus p​, find the following. ​a) The elasticity ​b) The elasticity at pequals89​, stating whether the demand is​ elastic, inelastic or has unit elasticity ​c) The​ value(s) of p for which total revenue is a maximum​ (assume that p is in​ dollars)

User Jstrong
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Answer:

The required elasticity is
E_p=(p)/(357-p).

The demand is inelastic.

The required value of p for which total revenue is maximum is 178.5

Explanation:

Consider the provided function.


D_p= 357-p


D_p=q= 357-p

Part (A) The elasticity ​

The elasticity of demand is:
E_p=(p)/(q) \cdot (dq)/(dp)


(dq)/(dp)=-1

But elasticity is always positive therefore,


E_p=(p)/(357-p)

Hence, the required elasticity is
E_p=(p)/(357-p).

Part (​b) The elasticity at p=89​, stating whether the demand is​ elastic, inelastic or has unit elasticity.

Substitute p=89 in above elasticity formula.


E_(89)=(89)/(357-89)


E_(89)=(89)/(268)

The above value is less than 1, therefore the demand is inelastic.

Part (C) The​ value(s) of p for which total revenue is a maximum​ (assume that p is in​ dollars).

For maximum revenue substitute E=1.


1=(p)/(357-p)


357-p=p


2p=357


p=178.5

Hence, the required value of p for which total revenue is maximum is 178.5

User Behkod
by
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