Suppose we now care about the long run decisions of a firm that has a production function of the form q = 4L^1/2 + K
Suppose w = 1 and r = 0.5
Assume that, at the beginning when w0 = 1 and r = 0.5, the firm chose to produce q0 = 20 units of output. Then, the wage increased to w1 = 2 and in consequence the firm chose to produce q1 = 10 units of output.
(a) Calculate the optimal choices of labor and capital after the wage change.
(b) Draw the old and new isocosts lines
(c) Calculate the scale effect
(d) Calculate the substitution effect
(e) Calculate the elasticity of substitution