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### Discrimination – Treating People Differently

© Allen C. Goodman 2000

Classical Model

- Becker (1957)
- People with discriminatory preferences must “pay” for their preferences.
- If whites prefer not to deal with blacks then it must cost them $.
- International trade model

Trade Model

- Suppose that W community is capital-rich.
- B community is capital-poor.
- Assume identical production functions whites exporting capital to black community.
- Blacks would export labor.
- MPKB > MPKW, so it pays to export capital.

MPK

MPKW

MPKB

E*

KW

CapitalW

Trade Model

- Suppose that W community is capital-rich.
- B community is capital-poor.
- Assume identical production functions whites exporting capital to black community.
- Blacks would export labor.
- MPKB > MPKW, so it pays to export capital.

MPK

MPKW

MPKB

Black gain

White gain

E*

KW

CapitalW

Trade Model

- Suppose that W have aversion to lending B their capital, due to discrimination.
- This “taste” means that their net return is reduced by some fraction

MPK

MPKW

MPKB

Taste for

Discrimination.

- Since the rectangle is a “payment for prejudices” then it does not count as income.

Black gain

White gain

E*

KW

CapitalW

Trade Model

- White income thus falls from yellow shaded area,
- To red area.

MPK

MPKW

- If tastes for discrimination fall, then income rises.
- Thus, we pay for our prejudices, and we can use the difference in return to capital, as a measure of discriminatory preferences.

MPKB

Taste for

Discrimination.

Black gain

White gain

E*

KW

CapitalW

Mathematics

- Krueger points out that other models are also consistent with observed differences in economic parameters. Start with a model where capital is perfectly mobile and labor is not, and that W society is capital-rich. Write

Yw = Q (Lw, Kw - E) + MPKbE

Yb = Q (Lb, Kb + E) - MPKbE

E = quantity of capital exported.

To maximize total output, you add equations:

Analytics

Yw = Q (Lw, Kw - E) + MPKbE

Yb = Q (Lb, Kb + E) - MPKbE

Y = Q (Lw, Kw - E) + Q (Lb, Kb + E)

dY/dE = -QKw + QKb = 0

QKw = QKb Equality of marginal products

Krueger’s Conjecture

- Krueger points out that other models are also consistent with observed differences in economic parameters. Start with a model where capital is perfectly mobile and labor is not, and that W society is capital-rich. Write

Yw = Q (Lw, Kw - E) + QKbE

dYw/dE = -QKw + QKb + E QKKb= 0

Since QKKb < 0, it means that the MP of capital in the white sector will be lower than that in the black sector.

QKb + E QKKb= QKw

Krueger’s Conjecture

QKb + E QKKb= QKw

Since capital is paid value of marginal product, the relationship of VMP to E is the demand curve for capital exported by whites.

d = (1/QKK)(QK/E) QKKE= QK/d

Substituting into above

QKb + QKb/d = QKw

QKw = QKb (1 + 1/d )

Krueger’s Conjecture

QKw = QKb (1 + 1/d )

Those familiar with trade theory will recognize this as an optimal tariff type of result. If whites behave as perfect competitors in their allocation of capital, they will do less well than if they impose an optimum tax on returns of exported capital, which would be:

tw = -1/(1 + d )

Becker’s calculation

Suppose:

Lb = 1, Kb = 1

Lw = 9, Kw = 150

Cobb-Douglas production function: Q = L2/3K1/3.

Optimal capital export would be 14.1 units (equalize K/L in each place). This would lead to B per capita incomes = 66% of white per capita incomes.

Since B income is monotonically related to E, we can relate E to discrimination.

Krueger points out that Yw would be maximized at 4.1 units of capital exported.

Urban aspects?

Naïve discrimination model would look at housing markets and say that discrimination in the market those who are bigoted would require higher rents from B to sell to them.

Standard competitive model would say that if this premium gets large enough it is easy for someone to buy W housing and convert it to B housing.

Easiest housing discrimination model postulates that B are willing to pay premium to live near W but that W are willing to live near B only if they get housing at a discount.

Bailey’s Model

Rent

In diseq’m B pay premium to live near W.

W who live near border get a discount.

Why is this diseq’m?

White

Black

Discount

paid by W

Because there are profits to be made.

As discount it pays to convert W housing to B housing.

Supply of B housing .

Border

Distance

Bailey’s Model

Rent

Supply of W housing decreases, increasing its price.

When does conversion stop?

Since only difference involves proximity to W, the valuation must be HIGHEST in W interior.

Lowest in B interior

White

Black

Discount

paid by W

Equilibrium

Border

Distance

Bailey’s Model

- How quickly does eq’m occur? Depends on:
- Neighborhood attachments - ethnic neighborhoods often more resistant to conversion
- Difficulty in converting housing from W to B.
- Ghetto population growth.

Testing

Often:

Hedonic model:

V = a + bH + cN + dR,

where H is housing, N is neighborhood, R is 1 if household were B, 0 if household were W.

If coefficient d is significantly +, suggests that B are being charged more.

Don’t want to use “% black” because that is a neighborhood rather than an individual attribute.

Findings

For 1960s housing mkts, there were premiums of 10 - 15%.

These seem to have declined some, although not entirely.

Must remember that well into 1950s there was gov’t and realtor sanctioned discrimination.

Equal housing rights legislation did not come into being until mid-1960s.

Price discrimination is not only form of discrimination. Suppose B are steered to certain neighborhoods -- does this reflect an assumption that people want to “live with their own kind” or discrimination?

Probably some of both!

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