Lauren’s utility function is uL(x1,x2) = min{x1, x2} and Humphrey’s utility function is uH (x1, x2)...

Lauren’s utility function is uL(x1,x2) = min{x1, x2} and Humphrey’s utility function is uH (x1, x2) = ?(x1) + ?(x2). Their endowments are eL = (4,8) and eH = (2,0).

a) Suppose Humphrey and Lauren are to simply just consume their given endowments. State the definition of Pareto efficiency. Is this a Pareto efficient allocation? As part of answering this question, can you find an alternative allocation of the goods that Pareto dominates the allocation where Humphrey and Lauren consume their respective endowment bundles?
b) As a function of market prices p = (p1,p2), determine Lauren’s and Humphrey’s optimal consumption choices.

c) Determine the market equilibrium price ratio, pˆ* = p1*/p2*. What are Lauren’s and Humphrey’s equilibrium consumption bundles?

Expert Solution

Rahul Sunny answered 2 years ago

Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the...

Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the price of good p2, the income is y. a. Derive ordinary demand functions. b. Draw indifference curves and budget line for the case when the price of good 1 is 10, the price of good 2 is 20, the income is 1200. c. Find the optimal consumption bundle.

Amy has utility function u (x1, x2) = min { 2(x1)^2x2, x1*(x2)^2 }. Derive Amy's demand...

Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand function for x1 and x2. For what values (if any) of m, p1, and p2 are the goods gross complements or gross substitutes of each other?

Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1,...

Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1, 3x2} a.What is the Nigella’s utility level if x1= 20 andx2= 3? b.Suppose P1= 1 andP2= 3(where P1is the price x1andP2is theprice of x2) and Nigella has an income of 18. What is Nigella’s budget constraint? Illustrate it in a graph c.Solve for the Nigella’s utility maximizing bundle of x1andx2.

Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer...

Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer Bridgit’s budget p1 x1 + p2 x2 = m p1 – price of stamps p2 – price of beer m – Bridgit’s budget a) What is Bridgit’s demand for beer and stamps? b) Is it true that Bridgit would spend every dollar in additional income on stamps? c) What happens to demand when Bridgit’s income changes (i.e. find the income elasticity)? d) What happens...

(a) Calculate the marginal utility of x1 and x2 for the following utility function u (x1;...

(a) Calculate the marginal utility of x1 and x2 for the following utility function u (x1; x2) = x 1 x 2 (b) What must be true of and for the consumer to have a positive marginal utility for each good? (c) Does the utility function above exhibit a diminishing marginal rate of substitution? Assume that and satisfy the conditions from Part b. (Hint: A utility function exhibits a diminishing marginal rate of substitution if the derivative of the marginal...

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be the income of the consumer, P1 and P2 the prices of good 1 and good 2, respectively. To simplify, normalize the price of good 1, that is P1 = £1. (a) Write down the budget constraint and illustrate the set of feasible bundles using a figure. (b) Suppose that m = £100 and that P2 = £10. Find the optimal bundle for the consumer....

Charlie’s utility function is U(x1, x2) = x1x2, where x1 and x2 are the Charlie’s consumption...

Charlie’s utility function is U(x1, x2) = x1x2, where x1 and x2 are the Charlie’s consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Charlie’s optimal consumption bundle. (Note that Charlie’s utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Charlie’s income have to be in order to...

1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's...

1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Amy's optimal consumption bundle. (Note that Amy's utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Amy's income have to be in order...

Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption...

Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Amy's optimal consumption bundle. (Note that Amy's utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Amy's income have to be in order to...

Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation...

Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation for Sara’s indifference curve that goes through the point (2,8). b. Suppose that the price of each good is 1 and that Clara has an income of 11. Draw her budget line. Can Sara achieve a utility of 36 with this budget? Why or why not? c. Evaluate the marginal rate of substitution MRS at (x1, x2) = (1, 5). Provide an economic interpretation...

Question