9. (5 points) Consider an entrepreneur who sells jewelry for $50 per piece. Clustering with similar entrepreneurs would increase labor costs, but it would allow some of the intermediate materials to be made at larger scales, thus reducing per-unit costs. (a) (1 point) Fill out the rest of the table below, finding the total cost per piece as well as the profit per piece for an entrepreneur depending on how many other entrepreneurs there are in a cluster. Number of entrepreneurs 1 2 3 4 5 7 Labor cost per piece 5 11 15 10 27 Cost of materials per piece 25 20 16 14 12 10 Total cost per piece Profit per piece (b) (1 point) Using the data in the table above graph the labor costs per piece, the costs of ma- terials per piece, and the total costs per piece as functions of the number of entrepreneurs in a cluster. (1 point) 40 35 25 20 15 10 5 0 2 (c) (1 point) Fill out the following table and graph, finding the profit gap between locating in clusters of more than one entrepreneur compared to locating to an isolated site (i.e., a cluster of size 1). That is, how much more profit will the firm earn in a cluster of multiple entrepreneurs compared to working in an isolated site (i.e., a cluster of size 1)? For thegraph, the x axis should be number of entrepreneurs in the cluster and the y axis should be the profit gap. Number of entrepreneurs 2 5 6 Profit gap (0) 15 10 5 -10 (d) (1 point) What would we expect the equilibrium cluster size to be? No explanation needed (yet). (e) (1 point) Briefly explain why the equilibrium cluster size would not be smaller than your answer in part (d)