3 Nokia sells a new budget cell phone Based on information p

3. Nokia sells a new budget cell phone. Based on information provided by the accounting department, the average variable cost is: AVC = $20 + Q The average fixed cost is: AFC = $4,000,000/Q where Q is the number of phones. The phone sells for $50. Show your work/thought process:

a. Find the total cost, average cost, and marginal cost equations.

b. At what level of output is average total cost minimized?

Solution

Nokia sells a new budget cell phone. Based on information provided by the accounting department, the average variable cost is: AVC = $20 + Q The average fixed cost is: AFC = $4,000,000/Q where Q is the number of phones. The phone sells for $50. Show your work/thought process:
a. Find the total cost, average cost, and marginal cost equations.
b. At what level of output is average total cost minimized?

Total Cost= Fixed cost+Variable cost
=(20+Q+4,000,000/Q)*Q

Average total cost= AVC+AFC
=20+Q+4,000,000/Q

MArginal cost= Change in total cost/change in quantity
This cab ne found by first derivative of total cost with respect to quantity

dtc/dQ=1-4,000,000/Q2

b)Average total cost minimized :

The output is found by differentiting the Average total cost and equating to zero.

dtc/dQ=1-4,000,000/Q2=0

Q=2000

The second derivative of above function is positive so the eqaution is minimized at Q=2000
So the required quantity is 2000 units