13. unit costs Ralph is exploring his understanding of various product costing models.

For this purpose he envisions a single product firm, along with three cost pools: direct labor, direct material, and overhead. Ralph writes down the following LLAs to describe these three pools: DL =

a ·q,DM = b · q and OV = c+d ·DL. DL denotes direct labor, DM direct material, and OV overhead. q denotes the units produced.

Finally,

a, b, c and d are constants. So the slope of the DL LLA is a, the intercept of the OV LLA is

c, etc.

Ralph also recognizes the actual costs will differ from those described by the noted LLAs. To accommodate this reality, Ralph next envisions the actual cost in each of the pools as actual DL =DL = a · q + ε1 actual DM = DM = b · q + ε2 actual OV =OV = c + d ·DL + ε3

ε1, then, is simply the difference between actual direct labor cost and that amount predicted by the LLA (given q units were actually produced).

Now suppose
q units are produced, and the actual costs accumulated in each cost pool are given by actual DL =DL = a ·
q + ε1 actual DM = DM = b ·
q + ε2 actual OV =OV = c + d ·DL + ε3 Further suppose normal volume is N units of output (i.e., q = N);

and when standard costing is used the standard cost is based on the originally specified LLAs. Determine Ralph’s unit cost (i.e., accounting cost per unit produced) assuming (1) standard, full costing;

(2) full, normal costing; (3) variable, normal costing; and (4) actual, full costing. Hint: the unit cost under standard variable costing is a + b + d · a.