A firm has the production function Q = LK. For this production function, MPL = K and

Question:

A firm has the production function Q = LK. For this production function, MPL = K and MPK = L. The firm initially faces input prices w = $1 and r = $1 and is required to produce Q = 100 units. Later the price of labor w goes up to $4. Find the optimal input combinations for each set of prices and use these to calculate the firm's price elasticity of demand for labor over this range of prices.