Suppose a hotel is profit-maximizing. It has one factor of production, which is the amount of labor (L) it hires. For each hour of labor, the firm pays a wage w. The production function is given by f(L) = L^1/2.

a. Suppose that in equilibrium, the wage rate is fixed at w = 7. Solve for the firm's optimal choice of how much labor to hire.

b. Imagine the government votes to increase the minimum wage to w = 10. What happens to employment in the firm?

c. Suppose the firm instead chooses to minimize the cost of producing a specific amount of q. Explain how this helps the firm maximize profits.