2. You own a company that writes financial literacy applications (apps) the vari

Question

2. You own a company that writes financial literacy applications (apps) the variable costs are as follows: Number of Apps Written for cellalar costs of operating your company are S12,000 per week and er week 2 Total Variable Costs $4,000 $8,000 S16,000 $32,000 $64,000 $128,000 $256,000 Average Average Variable Cost Average Marginal Cost Calculate total cost, average fixed cost, average variable cost, average total cost, and marginal cost for each number of apps written per week. What number of applications is the most efficient to write each week?

Explanation / Answer

TC = TFC + TVC

TC = 12,000 + cQ

where cQ = TVC = 4,000, 8000, 16000 and so on.

(I) TVC = 4000

TC = 12,000 + cQ = 12000 + 4000 = 16000

AFC = TFC / Q = 12000 / 1 = 12000

AVC = TVC / Q = 4000 / 1 = 4000

ATC = TC / Q = 16000 / 1 = 16000

MC = dTC / dQ = d(12,000 + cQ) / dQ = c

It is known that cQ = TVC

This implies, c = TVC / Q

Therefore, MC = c = TVC / Q = 4000 / 1 = 4000

(II) TVC = 8000

TC = 12,000 + cQ = 12000 + 8000 = 20000

AFC = TFC / Q = 12000 / 2 = 6000

AVC = TVC / Q = 8000 / 2 = 4000

ATC = TC / Q = 20000 / 2 = 10000

MC = dTC / dQ = d(12,000 + cQ) / dQ = c

Therefore, MC = c = TVC / Q = 8000 / 2 = 4000

(III) TVC = 16000

TC = 12,000 + cQ = 12000 + 16000 = 28000

AFC = TFC / Q = 12000 / 3 = 4000

AVC = TVC / Q = 16000 / 3 = 5333.33

ATC = TC / Q = 28000 / 3 = 9333.33

MC = dTC / dQ = d(12,000 + cQ) / dQ = c

Therefore, MC = c = TVC / Q = 16000 / 1 = 5333.33

(IV) TVC = 32000

TC = 12,000 + cQ = 12000 + 32000 = 44000

AFC = TFC / Q = 12000 / 4 = 3000

AVC = TVC / Q = 32000 / 4 = 8000

ATC = TC / Q = 44000 / 4 = 11000

MC = dTC / dQ = d(12,000 + cQ) / dQ = c

Therefore, MC = c = TVC / Q = 32000 / 4 = 8000

All other parts are similarly calculated.

The most efficient number of apps that can be written per week is where the average total cost is at the lowest. This is the point where the marginal cost and the average total costs meet. Thus, the most efficient number of apps per week will be where ATC = MC.

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