Price elasticity of demand for labor over range of prices

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A firm has the production function Q=L times K. 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 bar= 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 rm's price elasticity of demand for labor over this range of prices.

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