Exercises: Production costs and profit

Explain the difference between fixed costs and variable costs and write down how to calculate a firm's total cost. Give two examples of each type of cost in a café.

Classify these bakery costs as fixed or variable and justify each decision: shop rent, flour, the administrator's salary (the same payroll every month), yeast, and the wage of an assistant hired by the hour according to demand.

The figure shows the average cost (AC) and marginal cost (MC) curves of a firm, with their characteristic shape. The point where they intersect is marked with a question mark.

1. a) What does the marked point represent for the firm? Think about what happens to average cost at that level of production.
2. b) Reason why the marginal cost curve intersects the average cost curve precisely at its minimum, using the grade analogy: if your next mark is lower than your average, the average goes down.

A cake shop has fixed costs of $\$40\,000$ per month and a variable cost of $\$80$ per cake.

1. a) Calculate the total cost and the average cost if it produces $500$ cakes per month.
2. b) Calculate the average cost if it produces $1,000$ cakes and explain why the average cost falls as production increases.

A T-shirt company has recorded its total costs: producing $0$ units costs $\$2\,000$ (rent is paid regardless); $1$ unit, $\$2\,800$; $2$ units, $\$3\,400$; $3$ units, $\$4\,200$; and $4$ units, $\$5\,200$.

1. a) What is the firm's fixed cost? And what is the variable cost of producing $3$ units?
2. b) Calculate the marginal cost of the second, third and fourth units.
3. c) Calculate the average cost of producing $4$ units and explain how the marginal cost is evolving and why.

An ice cream shop sells $800$ ice creams per month at $\$60$ each. Its fixed costs are $\$20\,000$ per month and each ice cream costs $\$20$ in ingredients and packaging.

1. a) Calculate the total revenue, total cost and profit for the month.
2. b) The owner is considering staying open for one more hour each day: in that hour she would sell $50$ ice creams, and the extra staff and electricity would cost $\$1\,200$. Is it worth it for her? Reason your answer by comparing the revenue and cost of this decision.

The owner of a traditional bakery states: "If I invest in a continuous industrial kneading line, I will automatically reduce my unit costs and be able to sell much cheaper than the competition, securing the future of the business." Currently, he makes $1,000$ baguettes a day at an average cost of $\$0.80$ (with daily fixed costs of $\$500$ and a variable cost of $\$0.30$ per baguette). The new industrial technology would raise daily fixed costs to $\$1,400$, but it would reduce the variable cost to just $\$0.15$ per baguette. However, a market study estimates that maximum demand in his delivery area will not exceed $2,000$ baguettes per day at a price of $\$0.70$.

1. a) Numerically demonstrate whether the owner's statement is correct for his potential market: calculate the average cost per baguette with the new machinery if he produces and sells $2,000$ baguettes a day, and compare the daily economic profit of both options.
2. b) Calculate the exact daily production volume at which the industrial technology would become cheaper per unit than the traditional one (break-even point / point of indifference) and explain how this result relates to the minimum efficient scale.
3. c) Refute the owner's reasoning by analyzing two strategic risks or diseconomies of scale that threaten a small business that over-expands its technical capacity beyond the real size of its market.

The commercial director of a backpack factory proposes accepting an extraordinary order of $200$ units for a conference at a special price of $\$22$ per backpack. He presents the following argument to management: "Our average cost when manufacturing our usual output of $1,000$ backpacks is $\$18$, and we sell them in shops at $\$25$. Since they pay us $\$22$, we will make a clean $\$4$ per backpack above average cost, providing $\$800$ of additional net profit." However, the plant operates at the limit of its standard capacity: to manufacture those $200$ extra backpacks, overtime night shifts will be required, which will increase total variable costs from $\$12,000$ to $\$17,000$, while fixed costs remain at $\$6,000$.

1. a) Refute the commercial director's argument using precise calculations: determine the marginal cost per unit of the extraordinary order and calculate the real impact that accepting the offer would have on the firm's overall profit.
2. b) Explain the conceptual error made by the commercial director by making production decisions based on average cost instead of marginal cost.
3. c) Determine the minimum unit price at which the company could accept the order of the $200$ backpacks without reducing its prior profit, and state the marginalist rule for production optimisation.

The owner of an arepa food truck faces an especially difficult four-month winter season. His fixed costs are $\$3,000$ per month (vehicle lease, licences, and insurance, which must mandatorily be paid every month). For each arepa sold, he incurs $\$2.50$ in variable cost (ingredients and packaging), and the retail selling price is $\$6$. During the winter months, he expects to sell only $600$ arepas per month if he remains open at his usual location.

A novice consultant advises him: "Close down during the four winter months; since you are going to make losses, closing is the only way not to lose money." At the same time, a home delivery platform offers him the chance to operate from a ghost kitchen during that period: it guarantees sales of $1,000$ arepas per month at a reduced price of $\$5$, but the platform retains a $20\ \%$ commission on gross sales.

1. a) Evaluate the three options available for the four months (closing down completely, opening at the usual spot, or working with the platform): calculate the total accounting result for each alternative.
2. b) Use the shutdown rule criterion (short-run shutdown condition) to technically justify why the consultant's advice to close down to avoid losses is economically flawed compared to opening at the usual location.
3. c) Determine the minimum selling price that would mark the exact shutdown point for the food truck (below which it would indeed be advisable to suspend activity), calculate the monthly break-even sales volume to distinguish both concepts, and design an operational measure that would allow the business to lower said shutdown threshold.