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a) The production curve will look like in the upper part of Figure S.3.1.
b) The average product of labor is the total quantity of units produced divided by number of working hours. The marginal product of labor is how many extra units are produced if we add one more unit of labor:
AP_{L} = q/L
MP_{L} = Δq/ΔL
MP_{L} corresponds to the slope of the production function in the graph. APL corresponds to the slope from the origin to a certain point on the production curve.
c) The shapes of MPL and APL are given in the lower graph.
The most characteristic points on the production curve are points A, B, and C. Thecorresponding points below are labeled a, b, and c. In point A, the slope of the curve is the same as the slope of a line from the origin to point A. Consequently, MPL and APL have the same value there. In the corresponding point a, they intersect each other. Also note that APL slopes downwards on both sides of point a. In point B, the slope of the production curve is zero. Consequently, MPL intersects the X- axis at point b. In point C the production curve reaches its highest slope. Both to the left and to the rightof C the curve is less steep. Consequently, MPL reaches its maximum at c.
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