Costs, revenue and profit of the firm

The coffee shop "El Rincón" has the following costs: premises rent, coffee beans, fixed salary of the waiter, cardboard cups, monthly fee for the card payment terminal, and napkins. Classify them into fixed costs (they exist even if no one comes) and variable costs (they increase with every coffee sold), and explain what happens to each group in August when the neighbourhood is empty.

The 'Rizos' hairdresser's pays: the rent of the premises, the dyes and shampoos it uses with each customer, the hairdresser's fixed wage, the water and electricity (which rise with every wash), the insurance premium and the disposable towels.

1. a) Classify each cost as fixed or variable.
2. b) Explain what happens to profits in a quiet January, when fixed costs are still there but variable ones fall.

Define total revenue, total cost, and profit, and calculate them in this case: at the market, Julia sells $40$ bracelets at $3\ \text{€}$ each; the materials for each bracelet cost her $0,50\ \text{€}$ and the stall cost $20\ \text{€}$. How much revenue does she take in, how much does she spend, and how much profit does she make?

The bicycle repair shop "La Rueda" pays $900\ \text{€}$ per month in rent and utilities, regardless of how many repairs it carries out. It charges $30\ \text{€}$ per repair and parts cost an average of $10\ \text{€}$.

1. a) Calculate the margin left by each repair and how many repairs are needed per month to cover fixed costs.
2. b) If it carried out $60$ repairs this month, calculate its profit.
3. c) Explain what would happen to these figures if the landlord raised the rent.

The figure shows the total revenue (green line) and total costs (red line) of Nayara's group's T-shirt stall, based on the number of T-shirts sold. Each T-shirt is sold for $3\ \text{€}$, the materials for each cost $1\ \text{€}$, and the fixed costs of the stall are $60\ \text{€}$.

1. a) Do the calculations to find how many T-shirts must be sold for total revenue and total costs to be equal, and explain what the point marked with the question mark represents.
2. b) Explain what happens on the graph to the left and to the right of that point (where there are losses and where there are profits) and what would happen to the point if fixed costs increased.

The food truck "El Perrito Viajero" sells each hot dog for $5\ \text{€}$; the roll, sausage, and ingredients cost $2\ \text{€}$ per hot dog, and the monthly fixed costs (insurance, permits, fuel) are $600\ \text{€}$.

1. a) Calculate the profit if it sells $250$ hot dogs.
2. b) Calculate how many hot dogs it needs to sell per month to avoid losing money.
3. c) To attract customers, it is considering lowering the price to $4\ \text{€}$: calculate the new break-even point and advise whether this move could work out well or badly.

At the 'Trigo y Miel' bakery, each loaf sells at $1,30\ \text{€}$ and the ingredients cost $0,50\ \text{€}$; fixed expenses are $1.600\ \text{€}$ a month.

1. a) Calculate how many loaves must be sold a month to cover costs.
2. b) The price of flour rises and the cost per loaf goes up to $0,60\ \text{€}$: calculate the new break-even point.
3. c) Explain why a small rise in the variable cost moves the number of loaves needed so much.

The artisan bakery buys flour in sacks at $0,80\ \text{€}$ a kilo; if it buys a whole pallet, the kilo drops to $0,60\ \text{€}$. Each loaf takes $0,3$ kg of flour and it produces $3.000$ loaves a month.

1. a) Calculate how much flour it uses a month and how much it would save by buying the pallet.
2. b) Explain why producing on a large scale usually cheapens the cost per unit (economies of scale) and give another example from your neighbourhood.

The stationer's "El Tintero" sells $100$ backpacks a month for $25\ \text{€}$ each; each backpack costs $12\ \text{€}$ from the supplier, and its fixed costs are $1.040\ \text{€}$ per month. The owner is considering lowering the price to $22\ \text{€}$ and believes that doing so would increase sales to $150$.

1. a) Calculate the current profit.
2. b) Calculate the expected profit with the discount and decide whether it is worthwhile.
3. c) Calculate how many backpacks it would need to sell at $22\ \text{€}$ to make exactly the same profit as now, and assess the risk of the discount if sales do not rise as much as expected.

'If I lower the price, I'll sell more, so lowering it always pays off.' Answer with numbers: a shop sells $200$ phone cases at $10\ \text{€}$ with a cost of $4\ \text{€}$ per case, and is considering lowering the price to $8\ \text{€}$.

1. a) Calculate the current margin and how many cases it would have to sell at $8\ \text{€}$ to earn the same.
2. b) Explain why the statement fails almost always and say in which two specific cases lowering the price could pay off (stock that expires, entering a new market).