![]() The term on the right-hand side is calculated by differentiating the production function : This derivative is the total derivative of utility with respect to t, which may be calculated in the usual way via the chain rule: Which may be maximized with respect to t by equating its derivative to zero. Then utility is expressed as a function of the single variable t: One way to solve Alexei’s problem is to use the constraint to substitute for y in terms of t in the utility function. So we can write the constraint as an equation, which makes the problem easier to solve mathematically. But because his utility depends positively on t and y, we know that he will want to choose a point on the frontier. Sometimes in this sort of problem the constraint is written as an inequality:, which can be interpreted as saying that his choice must lie in the feasible set. This is an example of what is known in mathematics as a problem of constrained optimization. ![]() constrained optimization problem Problems in which a decision-maker chooses the values of one or more variables to achieve an objective (such as maximizing profit) subject to a constraint that determines the feasible set (such as the demand curve). Thus Alexei’s problem is to choose t and y to maximize subject to the constraint. As in Leibniz 3.4.1, if the production function is, where h is hours of study, the equation of the feasible frontier is: ![]() He wishes to maximize his utility given the constraint imposed by his feasible set of grades and free time. Alexei’s optimal choice of free time and exam grade.Īlexei’s utility function is : utility depends positively on hours of free time t and the exam grade y.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |