Draw output Y as a function of the labor input N given our usual assumptions about the production function (marginal product of labor is positive, but diminishing).
(a) What is the slope of the production function?
(b) Choose three points A, B and D on your production function such that N = 0 at point A, N = h at point D, and point B is between A and E in terms of the quantity of labor input used.
(c) How does the marginal product of labor MPN compare across the three points A, B and D.
(d) Use points A, B and D to plot output Y as a function of leisure l, exploiting that l = h − N, so that these points show up in your new figure.
(e) What is the slope of this new function? Explain. How does the slope of your function compare at points A, B and D?
(f) Given that C = Y − G, plot consumption C as a function on leisure l. Note where points A, B and D are on this new figure. How does the slope of this new function compare at points A, B and D?