Question

You own a small business that repairs furnaces and air conditioners. The market is competitive so you must charge the same price as all other firms - $50 per house visit. You can take on as many customers as you would like when you charge this price.

Your daily production function is given below, where K = the number of vans you have and L = the number of employees you have each day: ?? = ??(??, ??) = 10??2??1/2 (round down if you find a fractional unit of Q. For example, if you pick K and L such that Q=3.12 then round down to Q=3 in this case)

You currently lease 2 vans and cannot change this in the short run. The daily wage for one of your workers is w=$250, and since there is a competitive market for labor you cannot change this either. The daily rental rate on one van is r=$500.

1. If everything is the same in this problem except r = $500, how many workers do you want to hire? Show your calculations / explain.
2. Suppose again r = $500 but instead K = 3 (and everything else remains unchanged). How many workers do you want to hire? Show your calculations / explain. [Use the expression for MPL that I give above, or solve in Excel].
3. Using your answers to parts #1 and 2 above, what is the marginal benefit from the 3rd unit of K? What is the marginal cost of the 3rd unit of K?  
4. If you could choose to buy a 3rd unit of K or not, would you? You can't choose any other value: it's either 2 or 3. Explain.

Answer 1

Please refer to the image below for the solution. Remember that firms tend to hire the workers until there Marginal product from hiring a worker is equal to its cost i.e. wages, The same idea is used to solve for this question.