Question

Consider the model-management industry, with firms that supply human models for advertisements. Workers (models) vary in skin tone along the color wheel, which can be divided into 12 colors. Firms enter the market with a specific skin tone requirement for their models. If a model’s skin tone does not match the firm’s tone requirement, the model incurs a makeup cost to close the gap, with a cost of $3 for each unit of color shift. For example, to go from color #2 to color #4, the cost is $6. Given the scale economies of model management, each firm manages three models. The gross wage is $20.

1. 2.1 Smallville has six models, equally spaced on the color wheel at 12:00, 2:00, 4:00, etc. There will be firms in the city, with firm A at 12:00 and the other firm or firms at .

2. 2.2 Illustrate with a graph like the matching diagram in class (or Figure 3-4 in O’Sullivan).

3. 2.3 For the typical firm, the average mismatch is _____. The average net wage after makeup costs is

   skin tones and the average makeup cost is______ .

4. 2.4 Bigburg has twice as many models as Smallville. It will have firms. The average average makeup cost is . The average net wage after makeup costs is ____.

5. (Figure 3-4) .

   FIGURE 3-4 Skills Matching A: Four Skill Types B: Six Skill Types Skill 0 0 1/12 Worker1 Worker1 Firm A Firm C 10/12 2/12 Worker 6 Worker 2 6/8 worker 4 Worker 22/8 9/12 Firm E Worker5 Worker3 Firm B 8/12 4/12 Firm D Worker Worker 4 5/12 4/8 6/12 With four skill types, worker addresses are [0, 2/8, 4/8, 6/8. There are two workers per firm, so two firms will enter with skill requirements [1/8, 5/8), and the mismatch per worker is 1/8 With six skill types, worker addresses ane 0, 2/12, 4/12,6/12, 8/12, 10/12]. There are two workers per firm, so three firms will enter the market with skill requirements (1/12, 5/12, 9/12), and the mismatch per worker is 1/12.

Answer 1

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