American Ball Co. (ABC) is a rubber ball manufacturer. It has monthly fixed cost

Question

American Ball Co. (ABC) is a rubber ball manufacturer. It has monthly fixed costs of $2,000,000. Its marginal costs are $1.00 per ball.

•         What happens if sales fall by 20% from 2,000,000 to 1,600,000 balls per month?

•         What happens to average fixed costs (AFC) per widget and the marginal costs per ball?

•         If sales fall by 20 percent from 2 million balls per month to 1,600,000 balls per month, what happens to the AFC per ball, the MC per paper, and to the minimum amount that you must charge to break even on these costs?

Hint: Here Marginal Cost (MC) is constant, which implies that Average Variable Cost (AVC) is constant and equals MC. This does not imply Average Total Cost (ATC) is constant or has to equal MC. Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC). Divide through by the quantity Q, which implies TC/Q = FC/Q + VC/Q. This gives us ATC = AFC + AVC.

Explanation / Answer

Total cost (TC) = Fixed cost (FC) + (Q x MC)

(1)

Whn Q = 2,000,000:

TC ($) = 2,000,000 + (1 x 2,000,000) = 2,000,000 + 2,000,000 = 4,000,000

When Q = 1,600,000:

TC ($) = 2,000,000 + (1 x 1,600,000) = 2,000,000 + 1,600,000 = 3,600,000

So TC decreases by ($4,000,000 - $3,600,000) = $400,000 (= $400,000 / $4,000,000 = 0.1 or 10%)

(2)

When Q = 2,000,000:

AFC = $2,000,000 / 2,000,000 = $1

When Q = 1,600,000:

AFC = $2,000,000 / 1,600,000 = $1.25

AFC increases by $(1.25 - 1) = $0.25, or ($0.25 / $1) = 25%

MC remains unchanged at $1.

(3) Changes in AFC and MC are computed above.

In Breakeven, Revenue = TC, where revenue = Price (P) x Q

When Q = 2,000,000:

Revenue = $4,000,000

P x 2,000,000 = $4,000,000

P = $2 (Minimum price)

When Q = 1,600,000:

P x 1,600,000 = $3,600,000

P = $2.25 (minimum price)

So, minimum chargable price will increase by $(2.25 - 2) = $0.25, or by [($2.25 / $2) - 1] = 1.125 - 1 = 0.125, or 12.5%.

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