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1. Suppose there are several perfectly competitive firms producing widgets, and each firm has a production function given by
where Ew and Eb are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is then
Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each widget is $100.
a. Firm A does not discriminate. How many workers of each race would Firm A hire? How much profit does this non-discriminatory firm earn if there are no other costs?
b. Firm B discriminates against blacks with a discrimination coefficient of .25. How many workers of each race does this firm hire? How much profit does it earn?
c. Firm C has a discrimination coefficient equal to 1.25. How many workers of each race does this firm hire? How much profit does it earn?
d. What kind of discrimination are Firms B and C exercising?
i. Taste-based discrimination
ii. Statistical discrimination
iii. Both taste-based and statistical discrimination
iv. Cannot be determined
e. Consider a law that requires any given firm to pay its black workers the same wage as its white workers? How effective would this racial wage or employment gap in this model?
f. Suppose entrepreneurs can start new widget-producing firms using the same production function as existing firms. Also assume firms must shut down if they make negative profits. In the model above, how might free entry/exit in and out of the widget market help reduce the racial wage and employment gap over the long term?
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