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Answer :
Let's go through the problem step by step to determine the total revenue, marginal revenue product (MRP), and the number of pickers that should be hired if the wage rate is [tex]$15.00 per hour.
### Step 1: Calculate Total Revenue
The total revenue is calculated by multiplying the output of grapes (flats per hour) by the price of grapes per flat. Given that the price per flat is $[/tex]5.00, we can calculate the total revenue for each number of pickers:
- 0 Pickers: 0 flats × [tex]$5.00 = $[/tex]0.00
- 1 Picker: 10 flats × [tex]$5.00 = $[/tex]50.00
- 2 Pickers: 28 flats × [tex]$5.00 = $[/tex]140.00
- 3 Pickers: 43 flats × [tex]$5.00 = $[/tex]215.00
- 4 Pickers: 54 flats × [tex]$5.00 = $[/tex]270.00
- 5 Pickers: 61 flats × [tex]$5.00 = $[/tex]305.00
Total Revenue Table:
- [tex]$\$[/tex]0.00, \, \[tex]$50.00, \, \$[/tex]140.00, \, \[tex]$215.00, \, \$[/tex]270.00, \, \[tex]$305.00$[/tex]
### Step 2: Calculate Marginal Revenue Product (MRP)
The MRP is the additional revenue generated from hiring one more picker. It can be calculated as the change in total revenue when an additional picker is hired.
- From 0 to 1 Picker: (50 - 0) × 5 = [tex]$50.00
- From 1 to 2 Pickers: (140 - 50) × 5 = $[/tex]90.00
- From 2 to 3 Pickers: (215 - 140) × 5 = [tex]$75.00
- From 3 to 4 Pickers: (270 - 215) × 5 = $[/tex]55.00
- From 4 to 5 Pickers: (305 - 270) × 5 = [tex]$35.00
Marginal Revenue Product Table:
- $[/tex]0, \, \[tex]$50.00, \, \$[/tex]90.00, \, \[tex]$75.00, \, \$[/tex]55.00, \, \[tex]$35.00$[/tex]
### Step 3: Determine the Number of Pickers to Hire
To determine how many pickers to hire, compare the MRP to the wage rate. The company should hire pickers as long as the MRP is greater than or equal to the wage rate of [tex]$15.00 per hour.
By comparing:
- For 1 Picker: MRP = $[/tex]50.00 (≥ [tex]$15.00)
- For 2 Pickers: MRP = $[/tex]90.00 (≥ [tex]$15.00)
- For 3 Pickers: MRP = $[/tex]75.00 (≥ [tex]$15.00)
- For 4 Pickers: MRP = $[/tex]55.00 (≥ [tex]$15.00)
- For 5 Pickers: MRP = $[/tex]35.00 (≥ $15.00)
Since even with 5 pickers, the MRP is still greater than the wage rate, the result suggests hiring either zero or one picker as marginal revenue from a single picker barely reaches or surpass wage rate. In typical situations it's beneficial to go till the marginal value fall below wages.
Therefore, the optimal number of pickers to hire, in this scenario, is zero as interpreted from the final given output.
I hope this breakdown has made the solution clear! If you have any more questions, feel free to ask.
### Step 1: Calculate Total Revenue
The total revenue is calculated by multiplying the output of grapes (flats per hour) by the price of grapes per flat. Given that the price per flat is $[/tex]5.00, we can calculate the total revenue for each number of pickers:
- 0 Pickers: 0 flats × [tex]$5.00 = $[/tex]0.00
- 1 Picker: 10 flats × [tex]$5.00 = $[/tex]50.00
- 2 Pickers: 28 flats × [tex]$5.00 = $[/tex]140.00
- 3 Pickers: 43 flats × [tex]$5.00 = $[/tex]215.00
- 4 Pickers: 54 flats × [tex]$5.00 = $[/tex]270.00
- 5 Pickers: 61 flats × [tex]$5.00 = $[/tex]305.00
Total Revenue Table:
- [tex]$\$[/tex]0.00, \, \[tex]$50.00, \, \$[/tex]140.00, \, \[tex]$215.00, \, \$[/tex]270.00, \, \[tex]$305.00$[/tex]
### Step 2: Calculate Marginal Revenue Product (MRP)
The MRP is the additional revenue generated from hiring one more picker. It can be calculated as the change in total revenue when an additional picker is hired.
- From 0 to 1 Picker: (50 - 0) × 5 = [tex]$50.00
- From 1 to 2 Pickers: (140 - 50) × 5 = $[/tex]90.00
- From 2 to 3 Pickers: (215 - 140) × 5 = [tex]$75.00
- From 3 to 4 Pickers: (270 - 215) × 5 = $[/tex]55.00
- From 4 to 5 Pickers: (305 - 270) × 5 = [tex]$35.00
Marginal Revenue Product Table:
- $[/tex]0, \, \[tex]$50.00, \, \$[/tex]90.00, \, \[tex]$75.00, \, \$[/tex]55.00, \, \[tex]$35.00$[/tex]
### Step 3: Determine the Number of Pickers to Hire
To determine how many pickers to hire, compare the MRP to the wage rate. The company should hire pickers as long as the MRP is greater than or equal to the wage rate of [tex]$15.00 per hour.
By comparing:
- For 1 Picker: MRP = $[/tex]50.00 (≥ [tex]$15.00)
- For 2 Pickers: MRP = $[/tex]90.00 (≥ [tex]$15.00)
- For 3 Pickers: MRP = $[/tex]75.00 (≥ [tex]$15.00)
- For 4 Pickers: MRP = $[/tex]55.00 (≥ [tex]$15.00)
- For 5 Pickers: MRP = $[/tex]35.00 (≥ $15.00)
Since even with 5 pickers, the MRP is still greater than the wage rate, the result suggests hiring either zero or one picker as marginal revenue from a single picker barely reaches or surpass wage rate. In typical situations it's beneficial to go till the marginal value fall below wages.
Therefore, the optimal number of pickers to hire, in this scenario, is zero as interpreted from the final given output.
I hope this breakdown has made the solution clear! If you have any more questions, feel free to ask.
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