Answer to Question #212561 in Calculus for Akhona Klanisi

Question

8.Given the demand function P_d = 35 − Q²

and the supply function P_s = 3 + Q².

Calculate the producer surplus for the supply function.

 

1.      0,0

2.      33,3

3.      69,0

4.      42,7

Answer 1

Question

Given the demand function P_d =35-Q² and the supply function P_s =3+Q² .

Calculate the producer surplus for the supply function.

1.0,0

2.33,3

3.69,0

4.42,7

Solution;

At equilibrium, P_d =P_s

35-Q² =3+Q²

35-3 =2Q²

16=Q²

Q=4

Using Q=4,P_d =P_s=19

Producer surplus is given by;

P*Q -$\int$₀^Q(P_sdQ)

19(4) -$\int$₀⁴(3+Q²)dQ

76-[(3Q+Q³/3)|₀⁴

76-[3(4) +4³/3]

76-100/3

42.666666...

42.7

Answer;

4. 42,7