Exam 3: A Consumers Constrained Choice

If the utility function (U)between food (F)and clothing (C)can be represented as U = ,holding the consumption of clothing fixed,the utility will

A consumer is given the chance to buy a concert ticket for $50 and refuses.Later,that same consumer wins a free ticket to the concert.When asked to sell that ticket for $50,the consumer refuses,indicating that he would rather use the ticket himself.This is an example of

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.

Suppose Paul's utility depends on the amount of time spent playing on the Internet (x)and the amount of time playing video games (y),and his utility function is U(x,y)= 3x^0.2 y^0.8 He has 15 hours of free time to spend on these two activities each week,and his goal is to maximize his utility. a.Set up the Lagrangian for this constrained maximization problem. b.What are the necessary conditions for the optimum from the Lagrangian? c.What is the optimal amount of time spent surfing the Internet and playing video games each week?

A consumer's willingness to trade one good for another can be expressed by the consumer's

Assume the price of beer is $4,the price of pizza is $10 and the consumer's income is $250.Which consumption bundle will NOT be the consumer's choice?

-Max has allocated $100 toward meats for his barbecue.His budget line and indifference map are shown in the above figure.If Max's current MRS = -0.8,then Max is at point

The preferences for Californians can be represented by the following utility function: U(X,Y)= X^aY^1-a.The consumer faces the budget constraint I = p.X + q.Y,where I is the agent's income,and p and q are the prices.Suppose the government imposes a consumption restriction so that any person in the state is allowed to consume 50 units of electricity at most. a.If a = 0.25,I = 100,and both prices are equal to one,find the optimal consumption of gasoline and electricity by the agent.Is the electricity constraint binding? (Hint: solve the problem without the 50 ≥ X constraint and see if the solution satisfies the constraint.If your answer then does not satisfy 50 ≥ X,the solution must be 50 = X) b.How does your answer in part a.change if a = 0.75? Explain. c.On a graph,illustrate the answers to parts a.and b.

Joe's income is $500,the price of food (F)is $2,and the price of shelter (S)is $100.Which of the following bundles is in Joe's opportunity set?

Indifference curves cannot intersect.

-Max has allocated $100 toward meats for his barbecue.His budget line and an indifference map are shown in the above figure.Which of the following best describes Max's preferences?

If a consumer views the two goods they consume as perfect substitutes,the optimal bundle will be a corner solution.Explain.

Utility is the set of numerical values that

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.

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.

What is the difference between ordinal and cardinal measurement?

-Max has allocated $100 toward meats for his barbecue.His budget line and indifference map are shown in the above figure.If Max's current MRS = -1,then Max

The fact that most consumers are unable to describe their preferences in terms of a utility function implies that not all consumer preferences can be represented with utility functions.

Indifference curves are downward sloping because of the assumption of

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.