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HI, I'm stuck on the following question:

Suppose a small firm hires two types of labor:

blue-collar workers (E1) who have to be paid a salary w1 = 10, and white-collar workers (E2) who have to be paid a salary w2 = 20. The firm's production technology is

q = f(E1, E2) = ln(E1) + 2 ln(E2)

Assume that the firm takes the output price (p = 100) as given.

Write down the firm's maximization problem, and characterize the optimal labor demands (E1∗ and E2∗) as functions of the parameters (p, w1 and w2). How many workers of each type does the firm hire? Focus on solving the first order condition(s) and ignore the other optimality conditions.

Now suppose that the minimum wage increases from 7.5 dollars to 12.5 dollars. Assuming that this does not affect the wage of white collar workers nor the output price, how would the labor demand for each type of worker change?

How would your answer to the previous question change if you took into account that the minimum wage increase affects all firms in the industry, and not just the one small firm we are studying? Explain.

Show that for this particular type of production function, labor demand for either type of worker is neither elastic nor inelastic.

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