Question

Consider the advertisement industry, where firms use models (workers) to shoot advertise- ments. Suppose each model randomly comes with a different hair style, which can be classified into 12 types. In other words, think of the hair style wheel as a 12-hour clock, where models are evenly distributed around the wheel (#1, #2, ..., #12).

Each model works for only one firm, and each firm would require a single hair style. If a model's hair style does not match the firm's requirement, the hair style of the model must be re-designed in order to fit the requirement of the firm. The cost of re-styling is $6 for each unit of hair style gap. For example, to go from style #3 to style #2, the cost is $6; to go from style #5 to style #2, or from style #11 to style #2, the cost is $18. The gross wage for each model is $80. The net wage earned by each model is the gross wage less the adjustment cost. Suppose there are two cities. Smallville has 6 models and Bigburg has 12 models.

(a) Suppose each firm hires two models. How many firms will enter in Smallville and Big- burd, respectively?

(b) Recall that models are evenly distributed around the type wheel. For example, in Smal- lville, suppose that the 6 models are in positions (#2, #4, #6, #8, #10, #12). What is the adjustment cost for each model? What is the net wage in Smallville?

(c) Following the analysis in (b), what is the net wage in Bigburd?

(d) Now, suppose that each firm hires three models. How many firms will enter in Bigburd? What is the net wage in Bigburd?

(e) In this model, are workers better-off or worse-off in a city with clustering firms? What is the reason behind?

if possible, provide an explanation for my understanding. Thank you.