A firm is a price-taker in the labor market. The firm wants to choose the optimal level of labor to maximize profit. Let W be the unit price of labor, and assume that labor cost is the only cost of production:
a. Write the objective function in terms of L (labor). Hint: Use TR = TR[Q(L)] for total revenue.
b. Derive the first order condition (FOC) for profit-maximization in mathematical notations.
c. Derive the second order condition (SOC) for profit-maximization in mathematical notations.
d. Explain the economic meaning of the FOC and the SOC graphically and verbally.