Byzantium Bakery is located on State Street in Yore Town, Pennsylvania. It is a small operation known for its opulently crusty loaves. The owner, Leo Constantius, makes a practice of hiring interns from two well-known cooking schools. They remain at Byzantium Bakery for a three-month internship and then go on to full-time positions in five-star restaurants. Yeast of Eden Cooking College (YECC) and Xavier Unleavened Polytechnic (XUP) both produce highly competent graduates, and Leo has found that productivity is higher if he hires interns from both schools rather than just one. Over the past few years, he has compiled the production possibilities table that is shown below, in which Y represents the number of YECC bakers and X represents the number of XUP bakers. Y 7 6 5 4 3 2 1 0 X=> 9 11 12 12 11 9 5 0 0 21 22 22 21 19 16 12 7 1 Loaves of Bread per Hour (Q) 40 48 55 39 52 48 43 37 30 22 31 31 30 28 25 21 16 10 2 37 34 30 25 19 12 3 46 43 39 34 28 21 13 4 13 5 60 56 51 45 39 30 21 11 6 64 59 53 48 40 29 19 8 7 Leo is not sure how to use the information in the table, so he calls up a crusty old economist that he knows at Yore Town University and asks for advice. The economist sends out a student who recently did a wonderful job as an apprentice with Arcane Assemblies. Welcome to your new assignment. Use this information to solve Problems 8 through 12. Use the information in the table to construct an isoquant map. Plot isoquants for Q = 12, Q=21, Q=30, Q = 39, and Q = 48 on the graph below. 5 Number of YECC Bakers (Y) 6 A 3 N 1 0 Chapter 6: Problem 8 2 3 4 Number of XUP Bakers (X) 5 6 7 In the past, Leo has paid bakers from both colleges the same wage. Recently, however, the administration at XUP has insisted on a higher wage. The next group of YECC interns will charge $4 per hour while the XUP interns will charge $5 per hour. Leo wonders if he should stop hiring XUP interns entirely or, if he keeps on hiring both XUP and YECC interns, how many of each he should hire. 9. 10. Plot five isocost lines on the graph with the isoquant map from Problem 8. Each of the isocost lines should pass through the one point on each isoquant that represents the optimal combination of bakers. Next, determine the optimal number of bakers from each school, Leo's total cost of bakers, and the vertical and horizontal intercepts of the isocost lines and enter these values in the table below. Optimal Y Optimal X Total Cost Q=12 Q=21 Q=30 Q=39 = 48 Y Intercept X Intercept Plot the expansion path and the ridge lines on the graph in Problem 8. If the only inputs used by Byzantium Bakery are the two types of bakers, what are returns to scale like for the firm along the expansion path? Calculate the marginal rate of technical substitution (MRTS) in two ways for each of the five isoquants plotted on the graph in Problem 8. Begin at the optimal combination of X and Y on each isoquant. First, calculate the MRTS for a one unit decrease in X. Second, calculate it for a one unit decrease in Y. Enter your results in the table below. MRTS Decrease Y Decrease X Q=12 Q=21 Q=30 Q=39 Q=48 Is there a situation in which Leo should hire only YECC graduates? Is there a situation in which Leo should only hire XUP graduates? If Leo wants to produce 30 loaves per hour and the hourly cost of both types of graduates is the same, how many of each should Leo hire?