Question

Alicia’s Apple Pies is a roadside business. Alicia must pay $9.00 in rent each day. In addition, it costs her $1.00 to produce the first pie of the day, and each subsequent pie costs 50% more to produce than the one before. For example, the second pie costs $1.00 × 1.5 = $1.50 to produce, and so on.

1. Calculate Alicia’s marginal cost, variable cost, average total cost, average variable cost, and average fixed cost as her daily pie output rises from 0 to 6. (Hint: The variable cost of two pies is just the marginal cost of the first pie, plus the marginal cost of the second, and so on.)

2. Indicate the range of pies for which the spreading effect dominates and the range for which the diminishing returns effect dominates.

3. What is Alicia’s minimum - cost output? Explain why making one more pie lowers Alicia’s average total cost when output is lower than the minimum - cost output. Similarly, explain why making one more pie raises Alicia’s average total cost when output is greater than the minimum - cost output.

Answer 1

1. The various cost calculations are shown in the table below. The average costs are found by dividing the total by the output. The Marginal Cost is simply the difference in total cost for an extra unit of output.

Output	Fixed Cost	Variable Cost	Total Cost	Average Total Cost	Marginal Cost	Avg Variable Cost	Avg Fixed Cost
0	9	0	9	-	-	-	-
1	9	1.00	10	10	1	1	9
2	9	(1.00*1.50)=1.50	11.50	5.75	1.50	0.75	4.5
3	9	(1.50*1.50)=2.25	11.25	3.75	0.25	0.75	3
4	9	(2.25*1.50)=3.375	12.375	3.09375	1.125	0.84375	2.25
5	9	(3.375*1.5)=5.0625	14.0625	2.8125	1.6875	1.0125	1.8
6	9	(5.0625*1.5)=7.59375	16.59375	2.765625	2.53125	1.265625	1.5

2. The spreading effect is as output grows, it spreads over the fixed cost leading to a lower average fixed cost (AFC). In the given problem, this happens in the range of of zero to six pies, as we see that the AFC consistently decreasing over the entire range.

The Diminishing effect- the greater is the output, the less you would need the variable input on average, leading to a lower average variable cost (AVC). Here, this happens in the range of zero to three pies- the AVC lowers from infinty to 0.75, post which it starts to rise.

3. We know that the shut down point is the minimum of the AVC curve, i.e when average variable cost is just enough to cover my variable expenses like salary of employees. Fixed costs can be removed only after shutting down. In this example, it is at the production of the third pie, after which the AVC begins to increase. So, Alice's minimum cost output decision is at this point.

When output is lower than the minimum cost-output point (say, she is producing the second unit and going on the third)- here the average cost declines from 5.75 to 3.75 due to the diminishing returns of the variable input the impact of which is till the third unit, after which the marginal cost begins to rise.

Similarly, when the output is greater than the minimum choice, the average cost increases since the impact of diminishing returns have been fully exploited. Another addition to the variable input makes it costly on average. If you have four machines, the maximum labour employed will be four- an addition of a fifth person will lead to complications of divison of labour and in turn, make the production process expensive, on average as well as at the margin.