The demand function for drangles is qd p12 a What is the pr

The demand function for drangles is qd = (p+1)^-2

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

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

c. Write an expression for total revenue from the sale of drangles as a function of their price.

d. Find the revenue-maximizing price. Don’t forget to check the second-order condition.

Can you please show the work to get the answers, Thank You very much.

Explain each step thoroughly please

The demand function for drangles is qd = (p+1)^-2

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

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

= (-2(P+1)^(-3))*(P/(p+1)^-2)), where q =(p+1)^-2 (I have replaced q with the value as per the given demand function)

=(-2(p+1)^(-3+2))/p (Simplifying the exponents, when divided the powers get subtracted)

=-2p/(p+1)

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

-1 =-2p/(p+1))

2p = p+1

P=1

c. Write an expression for total revenue from the sale of drangles as a function of their price.

TR=P*Q (Total revenue is always equal to the price multiplied by the quantity sold)

P*(p+1)^-2 or (Inverse of a negative power makes it positive)

= P/(p+1)^2

MR=dTR/dQ

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

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

P=1

d. Find the revenue-maximizing price. Don’t forget to check the second-order condition.

(((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 which shows that TR is maximum at this point

P=1 Q=0.25

Maximum TR =0.25(1*0.25)