Yoda is a private tutor

1. Yoda's cost function for providing private lessons is

C(Q) = 9 + Q^??????2

(a) FC or Fixed Cost is the constant part of the cost function. Hence,

FC = 9

And, VC or Variable Cost is the variable part of the cost function which is a function of quantity (Q). Hence,

VC(Q) = Q^??????2

(b) AC or Average Cost is

AC(Q) = C(Q)/Q

or, AC(Q) = (9 + Q^??????2)/Q

or, AC(Q) = 9/Q + Q

AVC or Average Variable Cost is

AVC(Q) = VC(Q)/Q

or, AVC(Q) = Q^??????2/Q

or, AVC(Q) = Q

And, AFC kr Average Fixed Cost is

AFC(Q) = FC/Q

or, AFC(Q) = 9/Q

(c) MC or Marginal Cost is

MC(Q) = d[C(Q)]/dQ

or, MC(Q) = d[9 + Q^??????2]/dQ

or, MC(Q) = 2.Q

(d) We found that,

AC(Q) = 9/Q + Q

If AC(Q) is minimized, then we can write,

d[AC(Q)]/dQ = 0

or, -(9/Q^??????2) + 1 = 0

or, Q^??????2 = 9

or, Q = 3

AC(Q) is minimized when Q = 3.

Hope the solutions are clear to you my friend.