1. You produce diamond-studded dog collars. Your production function is: Y = AL^0.5K. Assume you have a large stockpile of diamonds and other collar material. Then the total number of collars you can produce in each hour (Y) is the product of your labor force (L in individuals) and capital (K, tables for working, space for tables, etc). "A" is a variable that captures any innovation you cancreateoradopttomakemorecollarsperhourwiththesamenumberofworkersandtables.
   1. Thanks to the recent surge in demand for diamond-studded collars, the equilibrium price of collars has increased to $100/collar. You are wondering if your company can supplymoretosellmoreatthisnew,higherprice.Youcanreallyonlychangeyourlabor force in the short-run. A calculus whiz on your economics team has determined that your MPL = 0.5AL^-0.5K. Say your "A" = 1, your current labor force is 100 people, and you have 50 units of capital (space for production, tables, glue guns, etc.). New workers will cost you $50/hr. Will you scale up? Why or why not? (2 points)
   2. Atwhatproductionpointwillitnolongerbeworthitforyoutoscaleup? Howmany laborers will you be employing? (2 points)
   3. You and your co-CEO anticipate that this demand for your product will continue next period.Yourco-CEOisreallyexcitedaboutyourboomingbusinessandsuggeststhatyou shouldscale-up for futureproduction by changing your capital stock. She statesthat the only options are to either buy more capital or invest in some new tech to make your current capital more productive. You suspect there is at least one other option for how to change your capital. What is it? (1 point). What key idea is your co-CEO missing? (1 point)