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Yoda is a private tutor. Yoda's cost function for providing private lessons is (Q) = 9+Q? a. Find Yoda's FC and VC(Q). (1 point) b. Find AC(Q), AVC(Q), and AFC(Q). (2 points) c. Find MC(Q). (1 point) d. Find the Q that minimizes AC(Q). (5 points)
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.