To calculate the marginal cost, we need to find the increase in total cost for producing one additional unit. Mathematically, the marginal cost for producing the [tex]\( n \)[/tex]-th unit is given by:
[tex]\[ \text{Marginal Cost for } n \text{-th unit} = \text{Total Cost for } n \text{ units} - \text{Total Cost for } (n-1) \text{ units} \][/tex]
Let's calculate the marginal costs step-by-step for each specified quantity of bikes:
### 1. Marginal Cost for the First Bike:
There is no previous cost to subtract from for the first bike, but it starts with 0 bikes and goes to 1 bike. Thus, the total cost for producing the first bike is the total cost for 1 bike:
[tex]\[
\text{Marginal Cost for the 1st bike} = \$80
\][/tex]
### 2. Marginal Cost for the Fourth Bike:
[tex]\[
\text{Marginal Cost for the 4th bike} = \text{Total Cost for 4 bikes} - \text{Total Cost for 3 bikes}
\][/tex]
[tex]\[
= \$130 - \$110 = \$20
\][/tex]
### 3. Marginal Cost for the Sixth Bike:
[tex]\[
\text{Marginal Cost for the 6th bike} = \text{Total Cost for 6 bikes} - \text{Total Cost for 5 bikes}
\][/tex]
[tex]\[
= \$210 - \$160 = \$50
\][/tex]
### 4. Marginal Cost for the Seventh Bike:
[tex]\[
\text{Marginal Cost for the 7th bike} = \text{Total Cost for 7 bikes} - \text{Total Cost for 6 bikes}
\][/tex]
[tex]\[
= \$270 - \$210 = \$60
\][/tex]
Summarizing the results:
- The first bike: \[tex]$80
- The fourth bike: \$[/tex]20
- The sixth bike: \[tex]$50
- The seventh bike: \$[/tex]60
