The demand for labor is given by L(w) = 1000 - .5w, where w is the minimum wage. Find the level of w that maximizes the total wage payment, wL(w). What is the wage-elasticity of labor demand at the maximizing minimum wage?

What will be an ideal response?

We maximize w(1000 - .5w), which occurs where the derivative is zero:
1000 - w = 0
Thus, w = 1000. The elasticity at that point is E = (dL/dw)(w/L) = .5(1000/500 ) = 1.

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