Chapter 2, Problem 17P

To determine

(a)

The total revenue function of the firm.

Answer to Problem 17P

$Totalrevenue=\text{ 200}x$

Concept used: Total revenue refers to the total amount of money collected from the sale of goods and services produced by a firm.

Calculation:

Let output be given by x units per year and Price be given by P.

Pick two points (250, 50000) & (1000, 100000)

Slope = 200

Then,

$Totalrevenueforxunitsperyear=200x$.

Conclusion:

$Totalrevenueforxunitsperyear=200x$.

Explanation of Solution

Concept used: Total revenue refers to the total amount of money collected from the sale of goods and services produced by a firm.

Calculation:

Let output be given by x units per year and Price be given by P.

Pick two points (250, 50000) & (1000, 100000)

Slope = 200

Then,

$Totalrevenueforxunitsperyear=200x$.

Conclusion:

$Totalrevenueforxunitsperyear=200x$.

To determine

(b)

The marginal cost of producing a given level of output.

Answer to Problem 17P

$Totalcost=\$100,000+\text{ 100}x$

Concept used: Total cost refers to the total cost of producing goods and services. It also included the variable cost of production and the fixed cost of production.

Calculation:

Let output be given by x and Price be given by P. Then,

$Totalcost=\$100,000+100x$

Marginal cost of the slope of the total cost line. Cost changes from $100,000 to $200,000, output changes from 0 units to 1000 units per year.

So,

$\begin{array}{l}Marginalcost=\frac{\$200,000-\$100,000}{1000-0}\hfill \\ =\frac{\$100,000}{1000}\hfill \\ =\text{ 100}\hfill \end{array}$

Marginal cost is $100 per unit.

Conclusion:

Marginal cost is $100 per unit.

Explanation of Solution

Concept used: Total cost refers to the total cost of producing goods and services. It also included the variable cost of production and the fixed cost of production.

Calculation:

Let output be given by x and Price be given by P. Then,

$Totalcost=\$100,000+100x$

Marginal cost of the slope of the total cost line. Cost changes from $100,000 to $200,000, output changes from 0 units to 1000 units per year.

So,

$\begin{array}{l}Marginalcost=\frac{\$200,000-\$100,000}{1000-0}\hfill \\ =\frac{\$100,000}{1000}\hfill \\ =\text{ 100}\hfill \end{array}$

Marginal cost is $100 per unit.

Conclusion:

Marginal cost is $100 per unit.

To determine

(c)

The break-even level of output.

Answer to Problem 17P

Break-even level of x is 1000 unit/year

Given information:

$Totalrevenueforxunitsperyear=200x$

$Totalcost=\$100,000+100x$

Concept used: Break-even point refers to the point where the firm earns zero economic profit. It is the point where total revenue is equal to the total cost of production.

Calculation:

Break-even point is given by,

$\begin{array}{l}Totalrevenue=Totalcost\hfill \\ 200x=\$100,000+100x\hfill \\ 100x=\$100,000\hfill \\ X=1,000\hfill \end{array}$.

Conclusion:

Break-even output is 1000 units.

Explanation of Solution

Given information:

$Totalrevenueforxunitsperyear=200x$

$Totalcost=\$100,000+100x$

Concept used: Break-even point refers to the point where the firm earns zero economic profit. It is the point where total revenue is equal to the total cost of production.

Calculation:

Break-even point is given by,

$\begin{array}{l}Totalrevenue=Totalcost\hfill \\ 200x=\$100,000+100x\hfill \\ 100x=\$100,000\hfill \\ X=1,000\hfill \end{array}$.

Conclusion:

Break-even output is 1000 units.

To determine

(d)

The profit of the company when 1500 units are produced and sold.

Answer to Problem 17P

Profit = $50,000

Given information:

$Totalrevenueforxunitsperyear=200x$

$Totalcost=\$100,000+100x$

Concept used: Profit refers to the amount of gain earned by the company. It is calculated as total revenue minus total cost of producing a given level of output.

Calculation:

If you sell 1500 units this year

$\begin{array}{l}Totalrevenue=200x\\ \text{= }200\times 1500\\ =\$300,000\end{array}$

$\begin{array}{l}Totalcost=\$100,000+100x\hfill \\ =\$100,000+100\left(1500\right)\hfill \\ =\$100,000+\$150,000\hfill \\ =\$250,000\hfill \end{array}$

$\begin{array}{l}Profit=Totalrevenue–Totalcost\hfill \\ =\$300,000-\$250,000\hfill \\ =\$50,000\hfill \end{array}$.

Conclusion:

Profit = $50,000.

Explanation of Solution

Given information:

$Totalrevenueforxunitsperyear=200x$

$Totalcost=\$100,000+100x$

Concept used: Profit refers to the amount of gain earned by the company. It is calculated as total revenue minus total cost of producing a given level of output.

Calculation:

If you sell 1500 units this year

$\begin{array}{l}Totalrevenue=200x\\ \text{= }200\times 1500\\ =\$300,000\end{array}$

$\begin{array}{l}Totalcost=\$100,000+100x\hfill \\ =\$100,000+100\left(1500\right)\hfill \\ =\$100,000+\$150,000\hfill \\ =\$250,000\hfill \end{array}$

$\begin{array}{l}Profit=Totalrevenue–Totalcost\hfill \\ =\$300,000-\$250,000\hfill \\ =\$50,000\hfill \end{array}$.

Conclusion:

Profit = $50,000.

To determine

(e)

The average and marginal cost of producing a given level of output.

Answer to Problem 17P

Average cost = $166.67

Marginal cost=$100

Given information:

$Totalrevenueforxunitsperyear=200x$

$Totalcost=\$100,000+100x$

Concept used: Marginal cost refers to the additional cost when one more unit of a good is produced. While, average cost is the cost per unit of output. It can be computed as total cost divided by the level of output.

Calculation:

Marginal cost is given by the change in total cost of production.

$\begin{array}{l}Costat1499units=\$100,000+\$100\times 1499\hfill \\ =249,900\hfill \end{array}$

$\begin{array}{l}Costat1500units=\$250,000\hfill \\ Changeincost=\$100\hfill \\ Changeinoutput=1\hfill \\ So,marginalcostis\$100.\hfill \\ Averagecost=\frac{\$250,000}{1500}=\$166.67\hfill \end{array}$.

Conclusion:

Average cost = $166.67

Marginal cost=$100.

Explanation of Solution

Given information:

$Totalrevenueforxunitsperyear=200x$

$Totalcost=\$100,000+100x$

Concept used: Marginal cost refers to the additional cost when one more unit of a good is produced. While, average cost is the cost per unit of output. It can be computed as total cost divided by the level of output.

Calculation:

Marginal cost is given by the change in total cost of production.

$\begin{array}{l}Costat1499units=\$100,000+\$100\times 1499\hfill \\ =249,900\hfill \end{array}$

$\begin{array}{l}Costat1500units=\$250,000\hfill \\ Changeincost=\$100\hfill \\ Changeinoutput=1\hfill \\ So,marginalcostis\$100.\hfill \\ Averagecost=\frac{\$250,000}{1500}=\$166.67\hfill \end{array}$.

Conclusion:

Average cost = $166.67

Marginal cost=$100.