Question

The cost of producing q units is C(q) = 4 + 5q + 2q2. Please answer the following questions (10 % each, 20 % total):

Answer 1

Answer:

(a) 11

(b) 13

Explanation:

The Total Cost is given in the question as follows:

Total Cost = C(q) = $4 + 5q + 2q^{2}$ ..................................................... (1)

Average cost (AC(q)) is calculated as Total Cost (C(q)) divided by quantity (q). This can be stated in mathematical equation as follows:  

$Average Cost = AC(q) = C(q)/ q = (4 + 5q + 2q^{2})/q$ .................... (2)

(a) When q = 2, the value of q which is 2 is substituted for it in equation (2) to obtain Average Cost as follows:

$Average Cost = AC(2) = C(2)/ 2 = [4 + 5(2) + 2(2^{2})]/2$

                                                    $= [4 + 10 + 2(4)]/2$

                                                    $= (4 + 10 + 8)/2$

                                                    $= 22/2$                                                    

$Average Cost = AC(2) = C(2)/ 2 = 11$

(c) Marginal Cost, MC(q) = C'(q), simply means change in the Total Cost, C(q), as a result of one unit change in the quantity. This can be obtained by differentiating the Total Cost, C(q), with respect to q. Since our Total cost function, C(q), is already given in equation (1) above, we can therefore differentiate it with respect to q and obtain MC(q) = C'(q) as follows:

$Marginal Cost = MC(q) = C'(q) = 5 + 4q$ .................................... (2)

The marginal cost of producing 2 units also implies that q = 2. We therefore 2 for q in equation (2) to obtain marginal cost of producing 2 units as follows:

$Marginal Cost = MC(q) = C'(q) = 5 + 4(2)$

                                                    $= 5 + 8$

$Marginal Cost = MC(q) = C'(q) = 13$

I wish you the best.