A proposed government project in a rural area with one-hundred unemployed would require the hiring of 20 workers. The project would offer wages of $12 per hour. Imagine that the reservation wages of the one-hundred unemployed fall between $2 and $20.
a. Estimate the opportunity cost of the labor required for the project assuming that the government makes random offers to the 100 unemployed until 20 of them accept jobs. (First, generate a list of the reservation prices of 100 persons according to the formula $2+$18u where u is a random variable distributed uniformly [0,1]. Second, work down the list to identify the first 20 workers with reservation wages less than $12. Third, sum the reservation wages of these 20 workers to get the opportunity cost of the labor used for the project.)
b. Estimate the opportunity cost of the labor required for the project assuming that the government can identify and hire the 20 unemployed with the lowest reservation wages.
c. Repeat part a. 15 times to get a distribution for the opportunity cost and compute its standard deviation.