Chapter 2, Problem 15P

To determine

(a)

Answer to Problem 15P

$\text{Total cost}=192,000+3840X$

$\text{Total revenue}=\$5,760X$.

Explanation of Solution

Given information:

Charges per camper or price charged = $480 per week.

Fixed costs = $192,000 per session.

Variable cost per camper = $320 per week.

Capacity = 200 campers.

Total cost is the cost of producing output. It includes both fixed and variable cost of production.

Calculation:

X = the number of campers per week.

The mathematical relationship is given by,

$\begin{array}{l}\text{Total cost}\text{=}\text{Fixed costs}+\left(\text{Variable cost per camper}\right)\times \left(\text{the number of campers}\right)\times \text{12}\hfill \\ \begin{array}{l}\text{Total cost}=192,000+320\times \left(X\right)\times 12\\ \text{Total cost}=192,000+3840X\end{array}\hfill \end{array}$

$\begin{array}{l}\text{Total revenue }=\left(\text{Charge per camper}\right)\times \left(\text{the number of campers per week}\right)\times \text{12}\hfill \\ \begin{array}{l}\text{Total revenue = 480}\times \left(X\right)\times \text{12}\\ \text{Total revenue = 5760}X\end{array}\hfill \end{array}$.

To determine

(b)

The break-even point for the company.

Answer to Problem 15P

100 campers to break-even.

Explanation of Solution

Given information:

Charges per camper or price charged = $480 per week

Fixed costs = $192,000 per session

Variable cost = $320 per week

Capacity = 200 campers.

Total cost is the cost of producing output. It includes both fixed and variable cost of production.

Break-even point refers to the point where the company is making zero profits. At this point the total revenue of the company is equal to its total cost.

Calculation:

At break-even point,

$\begin{array}{l}\text{Total revenue = Total cost}\hfill \\ 480\times X\times 12=192,000+320\times X\times 12\hfill \\ 5,760X=\$192,000+3,840X\hfill \\ 1,920X=\$192,000\hfill \\ X=100\hfill \end{array}$.

Conclusion:

To break-even 100 camper for a 12-week session.

To determine

(c)

The profit or loss of the company if it operates at 80% capacity.

Answer to Problem 15P

Profit = $115,200.

Explanation of Solution

Given information:

Charges per camper or price charged = $480 per week

Fixed costs = $192,000 per session

Variable cost = $320 per week

Capacity = 200 campers.

Total cost is the cost of producing output. It includes both fixed and variable cost of production. The profits of the company are its revenue left after deducting the total cost.

Calculation:

$\text{Capacity of the camp = 200 campers}$

If it operated at 80% capacity it means there are 160 campers in it. (80% of 200)

So, the profit of the company is,

$\begin{array}{l}\text{Profit = Total revenue – Total cost}\hfill \\ \text{Profit = }\$480\times 160\times 12-\$192,000–\$320\times 160\times 12\hfill \\ \text{Profit = }\$921,600–\$192,000– \$614,400\hfill \\ \text{Profit = }\$115,200\hfill \end{array}$.

Conclusion:

Thus, the company is making a profit of $115,200 at 80% capacity.

To determine

(d)

The average and marginal cost when the camp operates at 80% capacity.

Answer to Problem 15P

Average cost is $5,040 and Marginal cost is $3,840 per camper.

Explanation of Solution

Given information:

Charges per camper or price charged = $480 per week

Fixed costs = $192,000 per session

Variable cost = $320 per week

Capacity = 200 campers.

Total cost is the cost of producing output. It includes both fixed and variable cost of production.

Average cost is the per unit cost of production. It is obtained by dividing total cost by the total units produced.

Marginal cost is the addition to total cost when one more unit of an output is produced.

Calculation:

Total cost at 80% capacity is given by,

$\begin{array}{l}\text{Total cost = \$192,000 + }\$320\times X\times 12\hfill \\ \text{Total cost = \$192,000 + \$3,840}X\hfill \end{array}$

Marginal cost is the slope of the total cost equation. Therefore,

$\begin{array}{l}\text{Marginal cost is }\$3,840\text{ per camper}.\hfill \\ \text{Total cost for 160 campers }=\$806,400\hfill \\ \begin{array}{l}\text{Average cost per camper }=\frac{\$806,400}{160}\\ \text{Average cost per camper }=\$5,040\end{array}\hfill \end{array}$.

Conclusion:

Average cost is $5,040 and Marginal cost is $3,840 per camper.

To determine

(e)

Is it ethical to charge a different price to campers based on their family’s socio economic status.

No, it is not ethical to charge a different price to consumers.

Charging different rates to consumers for a same product is referred to as price discriminations. Discriminations of any sort can never be treated ethical. It leads to a wide disparity in the campers and is also considered illegal. There is no consumer surplus, all the surplus is the market is taken over by the producers.

However, some people argue that different rates will allow people with low willingness to pay also join the camp, as they will be charged low rates. It will lead to a greater participation in the camp.

Answer to Problem 15P

No, it is not ethical to charge a different price to consumers.

Explanation of Solution

Charging different rates to consumers for a same product is referred to as price discriminations. Discriminations of any sort can never be treated ethical. It leads to a wide disparity in the campers and is also considered illegal. There is no consumer surplus, all the surplus is the market is taken over by the producers.

However, some people argue that different rates will allow people with low willingness to pay also join the camp, as they will be charged low rates. It will lead to a greater participation in the camp.