Problem 1 You've been given the following production function: E2 =3E q 4 Assume the market price for the good is $10. (a) Calculate the Q, M PE, VM PE when E takes a value from 1-8 (ie - when E = 1, 2, 3,...). (b) Assume the wage rate (to) is $8. Based on your answers in part a, how many workers should the rm hire? Explain. (c) Now, using only the M PE, nd the optimal number of employees the rm should hire. Does it match what you found in part d? Hint: This will be an equation not a table. Problem 2 You've been given the following production function: q = E2K2 Let's assume the rental rate for capital (7') is $500, and the wage rate for labor (w) is $1,000. (a) If p = 10, what is the prot function? Hint: Do not solve. Your answer will be in terms of E and K. (b) Assume we are in the short-run and capital is xed at 4 (K = 4). What is the optimal level of employment (E) at that point? What is the rm's prot at this level? (0) If the rm was now in the long-run and wanted to produce 16,384 units (q = 16, 384), what is their cost minimzation problem? Dene it. (d) Finally, solve the cost minimization problem above. What is the optimal consumption of labor and capital? What is their prot at this point