In this exercise, I will show you how to plot some indifference curves for the utility function u(x, y) = xy. Carefully read and follow these steps.
(a) For each of the values x = 1, 2, 3, 4, 5, find the corresponding value of y such that u(x, y) = 5. Plot these points on a graph of the x, y coordinate plane.
(b) Find the formula for the slope of the indifference curve passing through any point (x, y). Calculate these slopes for each point from part (a).
(c) Plot the slopes from part (b) on the same graph by drawing a short line segment at each point with its corresponding slope. For example, at (1, y1), draw a small line segment with the slope of the indifference curve through (1, y1).
(d) On the same graph, approximate the indifference curve corresponding to u(x, y) = 5 by sketching a curve that passes through each of the plotted points from (a), matching the slope of the line segments from (c) at each point.
(e) Repeat parts (a)-(d), but now for u(x, y) = 10, using the same graph.