Question

Compute the average total cost, average variable cost, and marginal cost of producing $60$and $72$haircuts. Draw the graph of the three curves between $60$and $72$haircuts.

Short answer

ATC- Average Total Cost- $\$6.67$(for both $60$and $72$haircuts)

AVC- Average Variable Cost- $\$4$($60$haircuts), $\$4.44$($72$haircuts)

MC- Marginal Cost- $\$4$($60$haircuts), $\$6.67$($72$haircuts)

Step-by-step solution

Given information

Average total cost is the ratio of the total cost of production incurred to the total quantity produced.

ATC= TC/Q

Average Variable Cost is the ratio of total variable cost to the quantity produced.

AVC= TVC/Q

Marginal Cost is the additional cost incurred to produce one more unit of the output. In other words, it is the ratio of change in total cost to change in quantity.

MC= TC2-TC1/ Q2-Q1

Given -

Step2. Explanation

Average total cost:

$$\begin{gathered} ATC\left(72\right)=160+\frac{320}{72} \\ =\frac{480}{72} \\ =\$6.67 \end{gathered}$$

$$\begin{gathered} ATC\left(60\right)=160\frac{240}{60} \\ =\frac{400}{60} \\ =\$6.67 \end{gathered}$$

Average variable cost:

$$\begin{gathered} AVC\left(72\right)=\frac{320}{72} \\ =\$4.44 \end{gathered}$$

$$\begin{gathered} AVC\left(60\right)=\frac{240}{60} \\ =\$4 \end{gathered}$$

$$\begin{gathered} MC\left(60\right)=\frac{\left(400-320\right)}{\left(60-40\right)} \\ =\frac{80}{20} \\ =\$4 \end{gathered}$$

$$\begin{gathered} MC\left(72\right)=\frac{\left(480-400\right)}{\left(72-60\right)} \\ =\frac{80}{12} \\ =\$6.67 \end{gathered}$$

Graph-