Question 6.2

1. 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.)

    As shown in the accompanying table, the marginal cost for each pie is found by multiplying the marginal cost of the previous pie by 1.5. Variable cost for each output level is found by summing the marginal cost for all the pies produced to reach that output level. So, for example, the variable cost of three pies is $1.00 + $1.50 + $2.25 = $4.75. Average fixed cost for Q pies is calculated as $9.00/Q since fixed cost is $9.00. Average variable cost for Q pies is equal to variable cost for the Q pies divided by Q; for example, the average variable cost of five pies is $13.19/5, or approximately $2.64. Finally, average total cost can be calculated in two equivalent ways: as TC/Q or as AVC + AFC.

    Quantity of
    pies    		 Marginal
    cost of
    pie    		 Variable
    cost    		 Average
    fixed
    cost of
    pie    		 Average
    variable
    cost of
    pie    		 Average
    total
    cost of
    pie
    0 $0.00 — — —
    $1.00
    1 1.00 $9.00 $1.00 $10.00
    1.50
    2 2.50 4.50 1.25 5.75
    2.25
    3 4.75 3.00 1.58 4.58
    3.38
    4 8.13 2.25 2.03 4.28
    5.06
    5 13.19 1.80 2.64 4.44
    7.59
    6 20.78 1.50 3.46 4.96

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

    The spreading effect dominates the diminishing returns effect when average total cost is falling: the fall in AFC dominates the rise in AVC for pies 1 to 4. The diminishing returns effect dominates when average total cost is rising: the rise in AVC dominates the fall in AFC for pies 5 and 6.

  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.

    Alicia’s minimum-cost output is 4 pies; this generates the lowest average total cost, $4.28. When output is less than 4, the marginal cost of a pie is less than the average total cost of the pies already produced. So making an additional pie lowers average total cost. For example, the marginal cost of pie 3 is $2.25, whereas the average total cost of pies 1 and 2 is $5.75. So making pie 3 lowers average total cost to $4.58, equal to (2 × $5.75 + $2.25)/3. When output is more than 4, the marginal cost of a pie is greater than the average total cost of the pies already produced. Consequently, making an additional pie raises average total cost. So, although the marginal cost of pie 6 is $7.59, the average total cost of pies 1 through 5 is $4.44. Making pie 6 raises average total cost to $4.96, equal to (5 × $4.44 + $7.59)/6.