Cost Example

Easy DifficultyFE Engineering Economics

Given fixed and variable costs, find total cost, average cost per unit, and the incremental cost of one more unit.

Concept

Fixed cost (FC) : does not vary with output (e.g. rent, equipment). Variable cost (VC) : per-unit cost that applies to each unit produced. Total cost at quantity Q : T C = F C + (V C \times Q) . Average cost = T C / Q . Incremental cost of the next unit is the change in total cost. Sunk cost : past cost that cannot be recovered; ignore in forward-looking decisions. T C = F C + (V C \times Q) Average cost per unit = \frac{T C}{Q} = \frac{F C}{Q} + V C Notation: F C = fixed cost, V C = variable cost per unit, Q = quantity (units produced), T C = total cost.

A project has fixed cost F C = $5, 000 and variable cost V C = $30 per unit. Production quantity is Q units. Find: Total cost and average cost per unit when Q = 100 Incremental cost of producing the 101st unit

F C = $5, 000 V C = $30 per unit Q = 100 then 101

T C = F C + (V C \times Q) T C (100) = 5, 000 + (30) (100) = 5, 000 + 3, 000 = 8, 000 Avg at Q = 100 : \frac{8 , 000}{100} = 80 per unit

Incremental cost = change in total cost when increasing output by one unit. With linear variable cost, this equals V C . T C (101) = 5, 000 + (30) (101) = 8, 030 Incremental cost of 101st unit = T C (101) - T C (100) = 8, 030 - 8, 000 = 30

(1) At Q = 100 : total cost = $8, 000, average cost = $80 per unit. (2) Incremental cost of the 101st unit = $30 (equal to V C when variable cost is constant).

T C = F C + (V C \times Q) Average cost per unit = \frac{T C}{Q} = \frac{F C}{Q} + V C Notation: F C = fixed cost, V C = variable cost per unit, Q = quantity, T C = total cost. Sunk cost: already incurred, not relevant to future decisions