Question

A) The company will need to raise at least $300 million to bring their electric pickup truck to market. Suppose this is their fixed costs of production, and the marginal costs of production are $35,000 per vehicle. Calculate their ATC at Q=1,000; Q=5,000; and Q=10,000.

B) On a diagram depict this firms MC and ATC curve for the quantities listed in part a. Be sure that the relevant costs are clearly indicated on the $ axis.

C) Given the estimated price point for the Endurance, how many vehicles will Motors have to sell before they turn a profit?

Answer 1

(A) The company will need to raise at least $300 million to bring their electric pickup truck to market. This is their fixed cost.

Hence, Total Fixed Cost is

TFC = $300 million = $300000000

Now, the Marginal Cost of Production is given as

MC = $35000 per vehicle

Now, we will calculate the Total Cost from the above informations.

We know that,

MC is derivative of Total Cost (TC) i.e. a function of Q. Total Cost = TC(Q).

Hence, MC = dTC(Q)/dQ

or, dTC(Q) = MC.dQ

Now, putting MC = 35000, we get

dTC = 35000.dQ

Now, integrating both sides with respect to Q, we get

where, C is the integral constant.

or, TC(Q) = 35000.Q +C........(1)

Now, when Q=0, then TC(0) = Fixed Cost

Hence, TC(0) = F = 300000000

Hence, putting Q=0 in equation (1) we get

TC(0) = 35000×0 + C

or, 300000000 = 0 + C

or, C = 300000000

Hence, we get the Total Cost function as

TC(Q) = 35000.Q + 300000000.........(2)

Now, the Average Total Cost is

ATC = TC/Q

or, ATC = (35000.Q + 300000000)/Q

or, ATC = 35000 + 300000000/Q.........(3)

This is the Average Total Cost function. Now we will put the given values of Q in ATC and will calculate the values of ATC.

When, Q=1000

​​​​​​ATC = 35000+300000000/1000 = $335000

When, Q=5000

ATC = 35000+300000000/5000 = $95000

When, Q=10000

ATC = 35000+300000000/10000 = $65000

The following table contains the values.

Q	ATC($)	MC($)
1000	335000	35000
5000	95000	35000
10000	65000	35000

(B) Now, we will plot the MC and ATC curve for the three values of Q given in part A.

We will plot the values corresponding to the table above.

Here, X,Y,Z are the three points calculated in Part A.

(C)The estimated price level is not given in the question. Let us say the estimated price point is P°. When price level is P°, then

Total Revenue earned by selling Q motors is

TR = P°.Q

And, Total Cost is

TC = 35000Q + 300000000

Hence, The Total Profit of the company is

π = TR - TC

or, π = P°.Q - (35000.Q + 300000000)

Now, we will see where . Because, by satisfying this inequality, we will get the value of Q the company will start earning profit.

Hence, for

or, P°.Q - (35000.Q+300000000) 0

or, Q.(P°-35000) 300000000

or, Q 300000000/(P°-35000)

Hence, for an estimated price P°, the firm need to sell Q=300000000/(P°-35000) motors before they turn a profit.

Hope the solutions are clear to you my friend.