Economics questions! Pt. 2; help me!!?

Question

I'm stuck on this one and I was wondering if someone could give me a walk through for how this is solved. Here it goes:

The demand function for drangles is q(p)= (p + 1)'-2

1. What is the price elasticity of demand at price p?

2. At what price is the price elasticity of demand for drangles equal to -1?

3. Write an expression for total revenue from the sale of drangles as a function of their price. Use calculas to find the revenue-maximizing price. Don't forget to check the 2nd order condition.

Please help!

Answer 1

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Answer 2

1:

E=P*δQ/Q*δP

δQ/δP=((p + 1)^-2)' = -2*(1+P)^(-3)

E=(-2P*(1+P)^(-3))/Q

2:

(-2P*(1+P)^(-3))/Q=-1

-2P*(1+P)^(-3)=-Q

2P*(1+P)^(-3)=Q

2P*(1+P)^(-3)=(P+1)^(-2)

2P/(1+P)=1

2P=1+P

1P=1

P=1

3:

TR=Q*P = P/(P+1)^2

MR=0

MR=(TR)'

(P/(P+1)^2)' = 0

((1+P)^(-2))-2P/(1+P)^3=0

P=1

Second-order:

(((1+P)^(-2))-2P/(1+P)^3) '=

=(1+P)^(-3)*(6P/(1+P)-4)

P=1

6/16-4/8=3/8-1/2=-1/8

Second-order derivative is negative at this point - conclusion TR is at maximum point with price P=1 Q=0.25 TR(Max)=0.25

Answer 3

Dear I think there is some mistake of any sign in your question. Because in demand equation the sign of "P" should be negative which is not in your case. If we suppose that "-2" is multiplying with (P+1) then the answers of your questions are as follows:

1. Ed = (dq/dP)*(P/q)

2. Ed = -1 at P = -1/2

3. TR = P.Q = -0.5Q^2 - Q & Revenue maximizing price is    P = -0.5 or P = -1/2

I hope this will help you, But you need to check your question.

Answer 4

Too bad that I'm not helping you.