Consider again the two ways in which we can view the producer’s profit maximization problem. A: Suppose a homothetic production technology involves two inputs, labor and capital, and that its producer choice set is fully convex. (a) Illustrate the product

Consider again the two ways in which we can view the producer’s profit maximization problem. A: Suppose a homothetic production technology involves two inputs, labor and capital, and that its producer choice set is fully convex. (a) Illustrate the production frontier in an isoquant graph with labor on the horizontal axis and capital on the vertical. b) Does this production process have increasing or decreasing returns to scale? How would you be able to see this on an isoquant graph like the one you have drawn? (c) For a given wage w and rental rate r , show in your graph where the cost minimizing input bundles lie. What is true at each such input bundle? (d) On a separate graph, illustrate the vertical slice (of the production frontier) that contains all these costminimizing input bundles. e)Assuming output can be sold at pA, use a slice of the isoprofit plane to show the profit maximizing production plan. What, in addition to what is true at all the cost-minimizing input bundles, is true at this profitmaximizing plan? (f ) If output price changes,would you still profitmaximize on this vertical slice of the production frontier? What does the supply curve (which plots output on the horizontal and price on the vertical) look like? (g) Now illustrate the (total) cost curve (with output on the horizontal and dollars on the vertical axis). How is this derived from the vertical slice of the production frontier that you have drawn before? (h) Derive the marginal and average cost curves and indicate where in your picture the supply curve lies. (i) Does the supply curve you drew in part (f ) look similar to the one you drew in part (h)?