Exam 3: A Consumers Constrained Choice

A consumer has preferences given by the constant elasticity of substitution utility function: U(q₁,q₂)= (q₁.⁵ + q₂.⁵)² a.Write the Lagrangian for the consumer's maximization problem. b.Use the Lagrangian to solve for the optimal quantities in terms of the prices and income.

If the utility function (U)between food (F)and clothing (C)can be represented as U = ,the marginal rate of substitution of clothing for food will ________ if more food and less clothing are consumed.

-Max has allocated $100 toward meats for his barbecue.His budget line and indifference map are shown in the above figure.If Max is currently at point d,

-Max has allocated $100 toward meats for his barbecue.His budget line and an indifference map are shown in the above figure.Which bundle will Max choose?

A consumer's budget line for food (F)and shelter (S)is represented as F=250-5S.If the price of shelter increases by 2 and consumption of shelter remains constant at 20,how will consumption of food change?

Amanda consumes only two goods,X and Y.Her indifference curves satisfy the four standard assumptions.True or False: If she is indifferent between bundles (1,3)and (3,1),then bundle (2,2)must be strictly preferred.

For the following, please answer "True" or "False" and explain why -The slope of the budget line represents the rate at which the consumer is willing to trade one good for another at any given bundle.

The fact that consumers often react more to changes in the posted price of a good as compared to changes in the sales tax that is not posted is an example of

The assumption of completeness means that

Show that the utility functions V(X,Y)= XᵃY¹⁻ᵃ and U(X,Y)= a ln(X)+ (1-a)ln(Y)represent the same ordering of bundles.

If the prices of both goods and income increase by the same percentage,what will happen to the budget line?

If two goods,"x" and "y",are perfect substitutes,then which of the following best represents the utility function for the two goods?

-Max has allocated $100 toward meats for his barbecue.His budget line and an indifference map are shown in the above figure.What happens if Max's mother gives him 10 pounds of burger?

Explain why most indifference curves are convex.

Utility is the set of numerical values that

If the consumer's income increases while the prices of both goods remain unchanged,what will happen to the budget line?

Explain the difference between the marginal rate of substitution and the marginal rate of transformation.

For the following, please answer "True" or "False" and explain why. -Indifference curves on the same indifference map can have different shapes.

Howie consumes only beer (B)and donuts (D)each week with his $100 income.Beer costs $1,while donuts cost only 50¢.Howie has Cobb-Douglas preferences given by: U(B,D)= B(D-d) where d is the quantity of donuts that his neighbor Nord consumes.Assume throughout this question that Howie always consumes more donuts than Nord. a.How does Nord's beer consumption influence Howie's utility function? Specifically,compute and determine the sign of ∂U/∂d.Intuitively,what does this tell you about Howie's happiness and Nord's consumption of donuts? b.Holding d fixed,compute Howie's optimal consumption bundle of Beer and Donuts as functions of Nord's consumption of donuts,d. c.How does Nord's consumption of donuts affect Howie's optimal bundle? Specifically calculate and determine the sign of ∂B*/∂d and ∂D*/∂d where (B*,D*)is Howie's optimal consumption bundle.

What is the difference between ordinal and cardinal measurement?