Which of the following identifies the optimal usage of inputs by a profit-maximizing firm?

marginal product of labor/price of labor = marginal product of capital/price of capital
marginal revenue product of labor = marginal revenue product of capital
marginal cost of labor = marginal cost of capital
marginal product of labor/marginal product of capital = price of capital/price of labor
marginal product of labor = marginal product of capital = 0

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The common stock and debt of northern sludge are valued at $65 million and $35 million, respectively. investors currently require a return of 15.9% on the common stock and a return of 7.8% on the debt. if northern sludge issues an additional $14 million of common stock and uses this money to retire debt, what happens to the expected return on the stock? assume that the change in capital structure does not affect the interest rate on northern’s debt and that there are no taxes.

Afirm wants to hire a project manager (pm) at a salary of $100,000. 30% of pms have high ability, and 70% of pms have low ability. high ability pms generate $120,000 in revenue and low ability pms generate $80,000 in revenue. in addition to differences in productivity, high and low ability pms have different outside offers. if a high ability pm is not hired by the firm, she can work for another company at a salary of $80,000. if the low ability pm is not hired by the firm, she can work for another company for $70,000. high ability pms are also able to get a project management professional (pmp) certification at a cost of $1,000. low ability pms are unable to get a pmp certification (they would fail the test). the firm is not able to observe a pm’s ability, but is able to observe and verify whether or not the pm has a pmp certificate.(a) draw the extensive form of the game.expert answer