Let MP = Marginal Product, P = Output Price, And W = Wage, Then The Equation That Represents The Condition Where A Competitive Firm Would Hire Another Worker Is?

You wouldn't want to hire someone if their wage did not meet the requirement
  MP*P > W
Where MP is the additional number of units sold at price P, and W includes all wages, benefits, and other costs directly associated with the employee. MP must take into account any reduction in output from existing workers due to the addition of the worker of interest.