A Consumer Has the Following Utility Function for Goods X

question 45

Essay

A consumer has the following utility function for goods X and Y:
U(X,Y)= 5XY³ + 10
The consumer faces prices of goods X and Y given by p_x and p_y and has an income given by I.
a.Write out the Lagrangian expression for the consumer's utility maximization problem.
b.Write out the first order conditions necessary for maximizing utility subject to the budget constraint.
c.Show that the first order conditions imply the budget constraint and MRS condition.Provide the economic (i.e.non-mathematical)interpretation of these conditions - specifically,why are they necessary for the consumer to be at the optimal bundle?
d.Solve for the Demand Equations,X^*(p_x,p_y,I)and Y^*(p_x,p_y,I)
e.Show that the demand equations are homogeneous of degree zero.That is,show
X^*(cp_x,cp_y,cI)= X^*(p_x,p_y,I)
for any positive constant,c.

Apply theories and models like the theory of reasoned action, the theory of planned behavior, and the Transtheoretical Model to facilitate behavior change.

Recognize the importance of risk reduction and lifestyle choices in preventing diseases.

Identify the actions and interventions that promote health and prevent diseases.

Understand the factors influencing health behaviors and the application of models such as Pender's model and the health belief model.

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Definitions:

Constitution

A fundamental set of principles and precedents upon which a state or other organization is governed, often codified as a written document.

Commonly Agreed-upon

A term describing something that has been collectively accepted or approved by a majority.

Letters from an American Farmer

A series of essays written by J. Hector St. John de Crévecoeur in the late 18th century, depicting life in the American colonies and the emerging American identity.