Let's tackle the problem step by step.
### Part a:
1. Calculate the Marginal Revenue Product (MRP):
The MRP is calculated by multiplying the number of packages delivered per day by the revenue generated per package.
[tex]\[
\text{MRP} = 1,500 \text{ packages/day} \times \$0.10 \text{ per package} = \$150.00
\][/tex]
So,
[tex]\[
MRP = \$150
\][/tex]
2. Calculate the Marginal Resource Cost (MRC):
The MRC in this case is simply the cost of renting the vehicle per day, which is [tex]\( \$100 \)[/tex].
[tex]\[
MRC = \$100
\][/tex]
3. Should the firm add this delivery vehicle?
The firm should add the delivery vehicle if the MRP is greater than the MRC.
[tex]\[
\text{Since } 150 > 100, \text{ the firm should add the vehicle.}
\][/tex]
So, the answers for part a are:
[tex]\[
\begin{aligned}
&\text{MRP} = \$150, \\
&\text{MRC} = \$100, \\
&\text{Should the firm add this delivery vehicle?} \, \text{Yes (1)}.
\end{aligned}
\][/tex]
### Part b:
1. Recalculate the MRP:
The MRP remains the same as it is still calculated by the number of packages delivered per day times the revenue generated per package.
[tex]\[
\text{MRP} = 1,500 \text{ packages/day} \times \$0.10 \text{ per package} = \$150.00
\][/tex]
So,
[tex]\[
MRP = \$150
\][/tex]
2. Recalculate the MRC considering the increased rental cost:
The new MRC with the increased rental cost is [tex]\( \$200 \)[/tex] per day.
[tex]\[
MRC = \$200
\][/tex]
3. Should the firm add this delivery vehicle?
The firm should add the delivery vehicle if the MRP is greater than the MRC.
[tex]\[
\text{Since } 150 < 200, \text{ the firm should not add the vehicle.}
\][/tex]
So, the answers for part b are:
[tex]\[
\begin{aligned}
&\text{MRP} = \$150, \\
&\text{MRC} = \$200.
\end{aligned}
\][/tex]
