## 水曜日, 2月 27, 2019

### first-best allocation

ウィルソンについては
小平論考

Akerlof, George, (1970), “The Market for Lemons: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics 84, 488-500. Cho, In-Koo, and David Kreps (1987), “Signaling Games and Stable Equilibria,” Quarterly Journal of Economics 102, 179-221. Gibbons, Robert, (1992), Game Theory for Applied Economists, Princeton University Press.（福岡正夫，須田伸一訳『経済学のためのゲーム理論入門』，創文社，１９９５年）
Kreps, David, (1990), ACourse in Microeconomic Theory, Harvester Wheatsheaf. Mas-Colell, Andrea, Michael Whinston, and Jerry Green (1995), Microeconomic Theory, Oxford University Press. Riley, John, (1979), “Informational Equilibria,” Econometrica 47, 331-359.
Rothchild, Michael, and Joseph Stiglitz (1976), “Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information,” Quarterly Journal of Economics 90, 629-649.
Spence, Michael, (1973), “Job Market Signalling,” Quarterly Journal of Economics 87, 296-332.
Spence, Michael, (1974), “Competitive and Optimal Responces to Signaling; An Analysis of Efficiency and Distribution,” Journal of Economic Theory 8, 296332.

Wilson, Charles, (1977), “A Model of Insurance Markets with Incomplete Information,” Journal of Economic Theory 16, 167-207. Wilson, Charles, (1979), “Equilibrium and Adverse Selection,” American Economic Review 69 (papers and proceedings), 313-17.
Wilson, Charles, (1980), “The Nature of Equilibrium in Markets with Adverse Selection,” Bell Journal of Economics 11, 108-30.

スペンスの方が早いかも

### Another model

For a signal to be effective, certain conditions must be true. In equilibrium the cost of obtaining the credential must be lower for high productivity workers and act as a signal to the employer such that they will pay a higher wage.

In this model it is optimal for the higher ability person to obtain the credential (the observable signal) but not for the lower ability individual. The table shows the outcome of low ability person l and high ability person hwith and without signal S*:

Summary of the outcome for l and h with and without S*
PersonWithout SignalWith SignalWill the person obtain the signal S*?
lWoW* - C'(l)No, because Wo > W* - C'(l)
hWoW* - C'(h)Yes, because Wo < W* - C'(h)

The structure is as follows: There are two individuals with differing ability (productivity) levels.

• A higher ability / productivity person: h
• A lower ability / productivity person : l

The premise for the model is that a person of high ability (h) has a lower cost for obtaining a given level of education than does a person of lower ability (l). Cost can be in terms of monetary, such as tuition, or psychological, stress incurred to obtain the credential.

• Wo is the expected wage for an education level less than S*
• W* is the expected wage for an education level equal or greater than S*

For the individual:

Person(credential) - Person(no credential)  Cost(credential)  Obtain credential
Person(credential) - Person(no credential) < Cost(credential)  Do not obtain credential

Thus, if both individuals act rationally it is optimal for person h to obtain S* but not for person l so long as the following conditions are satisfied.

Edit: note that this is incorrect with the example as graphed. Both 'l' and 'h' have lower costs than W* at the education level. Also, Person(credential) and Person(no credential) are not clear.

Edit: note that this is ok as for low type "l":   , and thus low type will choose Do not obtain credential.

Edit: For there to be a separating equilibrium the high type 'h' must also check their outside option; do they want to choose the net pay in the separating equilibrium (calculated above) over the net pay in the pooling equilibrium. Thus we also need to test that:   Otherwise high type 'h' will choose Do not obtain credential of the pooling equilibrium.

For the employers:

Person(credential) = E(Productivity | Cost(credential)  Person(credential) - Person(no credential))
Person(no credential) = E(Productivity | Cost(credential) > Person(credential) - Person(no credential))

In equilibrium, in order for the signalling model to hold, the employer must recognize the signal and pay the corresponding wage and this will result in the workers self-sorting into the two groups. One can see that the cost/benefit structure for a signal to be effective must fall within certain bounds or else the system will fail.[4]

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ーー
 人々の豊かさの感覚を規定する要因は何か。新古典派と制度派、近代経済学とマルクス経済学を共通の分析枠組で位置づけた、実証分析に裏づけられた書。

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