Joseph Has the Utility Function U(F,H)=10F²H,where F Is the Quantity

question 68

Essay

Joseph has the utility function U(F,H)=10F²H,where F is the quantity of food he consumes per year and H is the quantity of housing per week.Suppose the price of food is $10 and the price of housing is $5,while Joseph has an income of $150/week.
a.Calculate Joseph's MRS as a function of the quantities F and H.
b.Write out Joseph's constrained optimization problem with the information provided.
c.Using the substitution method,solve for Joseph's optimal consumption bundle of food and housing.
d.Show that at the optimum,Joseph consumes the bundle along the budget constraint where MRS = MRT.

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Definitions:

Truth Table

A method of showing when compound logical expressions are true and when they are false by considering every possible assignment of truth values to propositions.

Propositional Reasoning

Drawing conclusions from premises that are in the form of true or false assertions.

Believability Effects

The impact of an individual's perceived credibility or believability on the acceptance and persuasion of their message.

Syllogistic Conclusion

The process of deriving a conclusion from two or more premises that are asserted or assumed to be true in logic.