Long-Run Optimization: Suppose you work as the administrator at a homeless shelter in the SF that wants to minimize the cost of finding jobs for 100 homeless people. The administrator has given you a $20,000 budget. Wage is $4,000 and rental rates for computers is $2,000. Suppose the production function is: q=20L-0.5L2+15K-0.5K2.
a) Suppose you hire 4 workers and rent 2 computers. (Don't use all the zeros. Use 20 for $20,000 same goes for wage and rent.)
i) Does this combination achieving the goal of 100 jobs for the homeless?
ii) Use the profit maximizing formula to see if this combination of workers and computers is efficient?
b) Find the quantity maximizing combination of K and L and how many jobs you will find for the homeless?