# Production in the long run - calculating wage and rental elasticity of demand

I have data for a business firm for two periods. The data include: output (Q), capital (K), labor (L), wage (W) and the rental rate of capital (R). Here they are:

    Period    K    L    W    R    Q
1        30    50   200  100  500
2        40    55   180  90   510


I need to find wage elasticity of demand, and, assuming "the same mathematical relationship exists for capital" (it is formulated in the task this way), rental elasticity of demand.

I have no idea how to handle this and need some direction, please. I know that wage elasticity of demand should be %change in labor / %change in wage, and rental elasticity of demand should be %change in labor / %change in rental rate of capital. However, it seems in this case it is not possible to apply these formulas right away.

I believe that it might be reasonable to compare labor L, wage W and rental rate of capital R using the same volume of output (Q). However, the production function is not given, so I have no idea how to arrive to comparable outputs.

I found that for equilibrium cases in the long run MP(L)/MP(K) = W/R. Moreover, W/R is the same in both periods, so it might be used for finding the answer. But I have no clues what to do further. Would be extremely grateful for any advice and direction.

• You say you're looking for the "wage elasticity of demand". Does this entail "conditional on fixing quantity produced" or not? Because initially, you don't specify this but later on you worry about it. Also: For which production functions is the elasticity independent of quantity produced? Is it fair to assume this? :) – FooBar Mar 5 '15 at 13:18
• Actually, I thought you were doing Macro. But on a firm level, yeah, I guess we can't just assume functional forms for the sake of simplicity. – FooBar Mar 5 '15 at 13:41
• Thank you for good question. Production functions with elasticity independent of quality - I'll research it and post my updates! I have no specific information regarding fixing quality, but I believe on a firm level we should assume changes in wage as independent variable, ceteris paribus, and measure changes in labor demand. Otherwise, if for example a firm decides to double production, it might need 2xlabor, but such change would not be applicable to calculate the elasticity of demand. – Olga Gnatenko Mar 5 '15 at 22:10
• Or, maybe I am making it overly complicated and should simply calculate %change in labor and divide it by %change in wage? Although, such straightforward reasoning seems not applicable in this context. – Olga Gnatenko Mar 5 '15 at 22:13