suppose that a monopolist hires a worker to produce x output for him and the monopolist pays the worker s wages for the work done. let the workers cost function be given as c(x)=x^2/2 and let the workers reservation utility be equal to zero.
a) if the monopolist chooses x and s to maximize his utility subject to the workers willingness to work, how much will the worker do?
To determine the optimal level of output chosen by the monopolist, we need to equate the worker's reservation utility to zero with the cost function.
The worker's reservation utility is the minimum level of compensation the worker requires to perform the job. In this case, it is assumed to be zero.
The cost function represents the cost to the monopolist of producing a given level of output. In this case, the cost function is given as c(x) = x^2/2.
Now, to find the optimal level of output (x) chosen by the monopolist, we set the worker's reservation utility equal to the cost function:
0 = x^2/2
We can solve this equation by multiplying both sides by 2:
0 = x^2
Now, taking the square root of both sides, we get:
x = 0
Therefore, the optimal level of output chosen by the monopolist to maximize his utility, subject to the worker's willingness to work, is zero. The monopolist will not have the worker produce any output in this case.