Question: Suppose that the table presented below represents production and cost data from a single firm. The table displays the level of labor (L) and capital (K) chosen by the firm in each year from 2009-2017, along with the input prices it faced (wages W and rental rates R). The table also displays the number of units of its product it need to produce (Q). You may assume that the production function that maps inputs into products, Q(K,L), does not change over time.
Year L K W R Q
2009 6 3 2010 3 5 2011 4 4 2012 11 7 2013 7 11 2014 14 5 2015 9 9 2016 13 19 2017 34 5
4 6 4 6 5 4 5 5 4 5 6 6 5 4 6 4 7 6 4 4 6 6 5 8 3 8 8
1A) What is the total cost of the firm in 2009?
1B) For which wage levels can the wage elasticity of labor demand be calculated? Why can't the wage elasticity be calculated for the other wage levels that appear in the table?
1C) Calculate the wage elasticity of labor demand when W = 5, R = 5, and Q = 4. Is labor demand inelastic or elastic with respect to the wage at this starting point?
1D) For which values of the wage can we estimate a wage elasticity of capital demand?
1E) Calculate the rental-rate elasticity of labor demand when W = 5, R = 4, and Q = 6.
1F). Calculate the marginal product of labor at L = 3,K = 5 (MPL(3,5)).
1G) Does the marginal product of labor decline as the level of labor increases? How do we know? (Hint: Use a capital level of K = 5)