Hi. I'd like to ask for (i) the solutions for letter (e) to help me understand; (ii) how the shaded region was arrived at and its meaning. Thank you.

246 PROFIT MAXIMIZATION (Ch. 19) 19.5 (0) A profit-maximizing firm produces one output, y, and uses one input, x, to produce it. The price per unit of the factor is denoted by w and the price of the output is denoted by p. You observe the firm's behavior over three periods and find the following: Period 1 2 2.5 3 .5 3 4 8 .25 'a) Write an equation that gives the firm's profits, #, as a function of the amount of input & it uses, the amount of output y it produces, the per-unit cost of the input w, and the price of output p. 7 = py - wx (b) In the diagram below, draw an isoprofit line for each of the three periods, showing combinations of input and output that would yield the same profits that period as the combination actually chosen. What are the equations for these three lines? y = x, y = 1 + .5x, y = 2 +.251. Using the theory of revealed profitability, shade in the region on the graph that represents input-output combinations that could be feasible as far as one can tell from the evidence that is available. How would you describe this region in words? The region that is below all 3 isoprofit lines . Output 12 10 Period 1 Period 2 Period 3 6 10 12 Input