Final answer:
The profit-maximizing quantity for Doggies Paradise Inc. is three units since it is the last quantity where marginal revenue exceeds marginal cost. Beyond three units, the cost of producing an additional unit exceeds the revenue it generates.
Step-by-step explanation:
To determine the profit-maximizing quantity for Doggies Paradise Inc., we need to calculate total revenue, marginal revenue, total cost, and marginal cost for each output level from one to five units. First, we calculate the Total Revenue (TR) by multiplying the number of units sold by the price per unit, which is $72. Marginal Revenue (MR) in a perfectly competitive market is equal to the price, so it remains at $72 for each additional unit. Total Cost (TC) is the sum of Fixed Costs (FC) and Variable Costs (VC). The Marginal Cost (MC) for each additional unit is the change in Total Variable Costs (TVC) as one additional unit is produced.
The table below summarizes these calculations:
1 Unit: TR = $72, MR = $72, TC = $100 + $64 = $164, MC = $64
2 Units: TR = $144, MR = $72, TC = $100 + $84 = $184, MC = $20 (increase in TVC from 1 to 2 units)
3 Units: TR = $216, MR = $72, TC = $100 + $114 = $214, MC = $30 (increase in TVC from 2 to 3 units)
4 Units: TR = $288, MR = $72, TC = $100 + $184 = $284, MC = $70 (increase in TVC from 3 to 4 units)
5 Units: TR = $360, MR = $72, TC = $100 + $270 = $370, MC = $86 (increase in TVC from 4 to 5 units)
Profit is maximized where MR = MC. Thus, the third unit is the profit-maximizing quantity because it is the last unit where MR ($72) is greater than MC ($30). The fourth unit has an MC of $70, which is lower than MR, but the fifth unit's MC ($86) exceeds MR, therefore reducing profit.