Tesla needs to take pricing and production decisions for the budgeting period 4.

Question

Tesla needs to take pricing and production decisions for the budgeting period 4. Use the Table below to answer the questions. The average unit costs and annual production volumes for the Lithium-ion battery used in the Model T are given in the table below. Tesla has been able to reduce its costs through experience effect in the past. Period Production 144,000 147,000 164,000 185,000 Unit Cost $150 $140 $135 1. Estimate the reduction in cost due to experience effects if Tesla produces 185,000 units in period 4. 2. Imagine Tesla cannot meet its pricing targets with the price you computed in Q1 and decides to increase production so that experience effects will lead to higher reduction in costs. How many units would they need to produce in Period 4 for the cost to fall to $128?

Explanation / Answer

Using Wright's cumulative average model, Y = aXb

where:

Y = Average cost per unit.

X = Number of units produced

a = Cost to produce first unit

r = learning rate,

b = log of the learning rate/log of 2. (slope of the function when plotted on log-log paper)

For period 1, Y = a*144000(ln(r)/ln(2)) = 150 ---(1)

For period 2, Y = a*(144000+147000)(ln(r)/ln(2)) = 140 ---(2)

For period 3, Y = a*(144000+147000+164000)(ln(r)/ln(2)) = 135 ---(3)

Dividing eq. (2) by (1), we get, a*291000(ln(r)/ln(2)) / a*144000(ln(r)/ln(2)) = 140/150

(291000/144000)(ln(r)/ln(2)) = 140/150

Taking log on both sides of the equation, we get,

(ln(r)/ln(2))*ln(291000/144000) = ln(140/150)

ln(r) = -0.06798

r = e-0.06798

r = 0.9343

Dividing eq. (3) by (2), we get,  a*455000(ln(r)/ln(2)) / a*291000(ln(r)/ln(2)) = 135/140

(455000/291000)(ln(r)/ln(2)) = 135/140

Taking log on both sides of the equation, we get,

(ln(r)/ln(2))*ln(455000/291000) = ln(135/140)

ln(r) = -0.0564

r = e-0.0564

r = 0.9452

Average learning rate = (0.9343+0.9452)/2 = 0.93975

Substituting this value of r in equation (1), we get, a*144000(ln(0.9398)/ln(2)) = 150 (instead of (1), we can also use (2) or (3)) . Solving it for a, we get,

Cost ro produce first unit, a = 435

Cumulative production for period 4 = 144000+147000+164000+185000 = 640,000

Using the learning rate as determined above, average cost for period 4 = 435*640000(ln(0.93975)/ln(2)) = $ 131.21

1. Reduction in cost due to learning effect = 135-131.21 = $ 3.79

2. Cumulative numbe of units upto period 4 be X, so 435*X(ln(0.93975)/ln(2)) = 128 , solving it for X, we get,

X = (128/435)ln(2)/(ln(0.93975)

= 843485

Units to produce in period 4 = 843485 - (144000+147000+164000) = 388,485 units

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.