Suppose that a developer is choosing tenants for a shopping center. There are four possible tenants: a department store, a toy store, a shoe store, and a hardware store. If each store were to be located in isolation outside a shopping center it would earn a certain level of gross profit per period ( this is the level of profit before subtracting out space rent). In addition, each store requires a certain number of square feet of floor space, which is the same regardless of whether or not it locates in a shopping center. The relevant values for each store type are as follows: Gross profit in Required square footage 9,000 1,000 isolation Department store Toy store $100,000 $11,200 $7,800 $7,000 800 Shoe store Hardware store 1,100 When the stores are located together each store earns a greater gross profit from the additional customer traffic generated by the nearby locations of other stores. The increase in gross profit for each store type ("affected store type") resulting from the presence of other store types ("added store type") is as follows: Added store type Department Affected store type Department Toy Shoe Toy $6,000 $8,000 Shoe Hardware $1,000 $600 $300 $2,000 $2,000 $1,000 $200 $500 $400 $200 Hardware qual to each store's gross profit, leaving Suppose that the shopping center developer charges a rent the store with a net profit of exactly zero. Total rent from the shopping center is then equal to the total gross profit of all its stores. The developer's profit is thus equal to total gross profit of all 2 Suppose that the shopping center developer charges a rent equal to each store's gross profit, leaving the store with a net profit of exactly zero. Total rent from the shopping center is then equal to the total gross profit of all its stores. The developer's profit is thus equal to total gross profit of all stores in the center minus the cost of providing space). Finally, suppose that, owing to high-quality construction and the need to provide common space around the stores, the construction cost for the shopping center space is high. In particular, suppose that the cost per period per square foot of store foot space is $10. (a) Give an intuitive explanation for the pattern of incremental profits from the presence of other stores in the second table above. (b) Suppose the developer were to construct a single-store shopping center ( a contradiction in terms, perhaps). There are four types of such centers ( a department store alone, a toy store alone, and so on). Using the information above, compute the developer's profit from each of these four types of centers. (c) Next compute the developer's profit from the various types of two-store shopping centers (i.e., department store plus shoe store, department store plus toy store, and so on; how many possibilities are there?) (d) Finally, compute profits form the various types of three-store centers and from the single type of four-store center. (e) Comparing your answers from (b), (c), and d), identify the optimal shopping center (the one yielding the highest profit to the developer). Explain intuitively why this particular collection of stores is optimal
