Consider the demand equation x+1/3p = 20 0 < or equal to p < or equal to 60, whe
ID: 3289074 • Letter: C
Question
Consider the demand equation x+1/3p = 20 0 < or equal to p < or equal to 60, where x = # of units, p is the unit price in $.
a) Find the elasticity of demand function. Use it to determine if at a price of $20, the demand is elastic, unitary, or inelastic. If the price was increased slightly from $20, would the revenue increase or decrease.
b) Find the revenue as a function of p: R(p).
c) Determine the intervals where the revenue is increasing and the intervals where it is decreasing. Should your sign graph to justify your answer.
d) At what price will the Revenue be a maximum?
e) What is the maximum Revenue?
f) What is the marginal revenue function? Also, find the marginal revenue when the price is $15. Interpret your answer.
I would appreciate it if the work could be shown so I can see how to get to the answers. This problem is really stumping me
Explanation / Answer
a)elasticity= (-dx/dp)*(p/x)= -(-1/3)*(1/2)=1/6
b)revenue=p*x=p*(20-p/3)=20p-p^2/3
d)for maximum revenue
d(20p-p^2/3)/dp=0
20-2p/3=0 ==>p=$30
e) maximum revenue=20*30-30^2/3 =$300
f)marginal revenue=d(20p-p^2/3)/dp=20-2p/3
at p=$15
marginal revenue=20-2/3*15=$10