$($Use the code from below to form the image$)$:

import numpy as np

import matplotlib.pyplot as plt

# Define the function for r$*$

def r$\_$star$($s$)$:

k $=(2\mathrm{.}5*(1+$ s$))**(-1/0\mathrm{.}6)$

return $1/(1+$ k$)$

# Define the range for s

s$\_$values $=$ np$.$linspace$(-1,10,400)$

r$\_$values $=[$r$\_$star$($s$)$ for s in s$\_$values$]$

# Plot the function

plt$.$figure$($figsize$=(10,6))$

plt$.$plot$($s$\_$values, r$\_$values, label$=$r$\text{'}$$r$^*=$ f$($s$)$$$\text{'})$

plt$.$xlabel$(\text{'}$Subsidy rate, $s$$\text{'})$

plt$.$ylabel$($r$\text{'}$Optimal ratio of labor hours, $r$^*$$$\text{'})$

plt$.$title$(\text{'}$Optimal Ratio of Labor Hours as a Function of Subsidy Rate'$)$

plt$.$axhline$(0,$ color$=$'black', linewidth$=0\mathrm{.}5)$

plt$.$axvline$(0,$ color$=$'black', linewidth$=0\mathrm{.}5)$

plt$.$grid$($color$=$'gray', linestyle$=\text{'}--\text{'},$ linewidth$=0\mathrm{.}5)$

plt$.$legend$()$

plt$.$show$()$