Question

In the short run, a firm's total costs of producing $100$units of output equal $10,000$. If it produces one more unit, its total costs will increase to $10,150$.

a. What is the marginal cost of producing $101$instead of $100$units of output?

b. What is the firm's average total cost of producing $100$units?

c. What is the firm's average total cost of producing $101$units?

Short answer

(a) The marginal cost of producing $101$instead of $100$units of output is$150$

(b) The firm's average total cost of producing$100$unitsrole="math" localid="1651839681224" $10000$

(c) The firm's average total cost of producing$101$units is$10150$

Step-by-step solution

Given Information (part a, b and c)

Producing units$=100$to $101$

The total cost $10000$increases upto $10150$

To find the marginal cost and firm's average total cost.

Find the Marginal cost (part a).

The marginal cost of producing the ${101}^{th}$unit can be calculated by taking into account the additional cost of production.

The total cost of producing $100$units is $10,000$, with an additional unit costing $10,150$. The following is a calculation of the marginal cost of producing the ${101}^{th}$unit of output.

$$\begin{gathered} M{C}_n=T{C}_n-T{C}_{n-1} \\ M{C}_{101}=10150-10000 \\ M{C}_{101}=150 \end{gathered}$$

Therefore, the marginal cost will be$150$

Find the firm's average total cost of producing 100 units (part b).

The average total cost is calculated by combining the total cost as well as the number of units produced. The total cost of producing $100$units is $\$10,000$.

As a result, the average total cost is

$$\begin{gathered} =100\left(\frac{10000}{100}\right) \\ =10000 \end{gathered}$$

Find the firm's average total cost of producing 101 units (part c).

The total cost and the number of total production units can be used to calculate the average total cost of producing $101$units.

The total cost of manufacturing $101$units is $10,150$. As a result, the average total cost is

$$\begin{gathered} =100\left(\frac{10150}{100}\right) \\ =10150 \end{gathered}$$