Question

What would be the total price ABC should pay for the 350 units for an 80% learning curve for labor, and for a 90% learning curve for labor? What % difference is this between the two assumptions of learning curves

Answer 1

According to Wright's Model,

Y = aX^b

Y = the cumulative average cost per unit.
X = the cumulative number of units produced.
a = cost incurred to produce the 1st unit.
b = log of the learning curve rate/log of 2.

A)

For an 80% learning curve for labor,

The total cost for all the units = X*Y

X*Y = X*aX^b

X*Y= a*X^b+1

for 80% learning curve rate, b = log .8/log 2 = -.322

The total cost for all the units = a*X^1-0.322

=a*X^0.678

=a*350^0.678

=50.073*a

B)

For an 90% learning curve for labor,

The total cost for all the units = X*Y

X*Y = X*aX^b

X*Y= a*X^b+1

for 80% learning curve rate, b = log .9/log 2 = -0.152

The total cost for all the units = a*X^1-0.152

=a*X^0.848

=a*350^0.848

=143.67*a

C)

% difference is this between the two assumptions of learning curves?

= ?[ 2(143.67*a? - 50.073*a?) / (143.67*a? + 50.073*a)]* 100

= 0.966 * 100

= 96.6%