Question: A representative firm produces output Y with the production function Y = zH +L, where H and L are high-skilled and low-skilled labor, respectively, and

A representative firm produces output Y with the production function Y = zH +L, where H and L are high-skilled and low-skilled labor, respectively, and z > 1 captures the productivity of high-skilled labor. (a) Show that the production function displays constant returns to scale. Assume that the representative firm hires high- and low-skilled labor in competitive markets. The hourly wage for high-skilled labor is wH and the hourly wage for low-skilled labor is wL. (b) Show that the representative firm makes zero profits. (c) Calculate the ratio of high-skilled wage to low-skilled wage, i.e., wH/wL. Is wH/wL increasing or decreasing in z? Explain. (d) Draw the labor demand curve for high-skilled and low-skilled labor in the same graph with wH and wL on the y-axis and H and L on the x-axis. [Hint: Recall that z > 1.]

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