Question

In: Economics

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.

Solutions

Expert Solution


Related Solutions

Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, 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?
Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The...
Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The price of good 1 is P1, the price of good 2 is P2, and his income is $m a day. The price of good 1 suddenly falls. (a)Represent, using a clearly labelled diagram, the hicks substitution effect, the income effect and the total effect on the demand of good 1. (b) On a separate diagram, represent using a clearly labelled diagram, the slutsky substitution...
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...
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.
(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...
Assume a consumer has the utility function U (x1 , x2 ) = ln x1 +...
Assume a consumer has the utility function U (x1 , x2 ) = ln x1 + ln x2 and faces prices p1 = 1 and p2 = 3 . [He,She] has income m = 200 and [his,her] spending on the two goods cannot exceed her income. Write down the non-linear programming problem. Use the Lagrange method to solve for the utility maximizing choices of x1 , x2 , and the marginal utility of income λ at the optimum.
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...
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....
Suppose that a consumer has a utility function U(x1,x2) = x1 ^0.5 x2^0.5 . Initial prices...
Suppose that a consumer has a utility function U(x1,x2) = x1 ^0.5 x2^0.5 . Initial prices are p1 =1and p2 =1,andincomeism=100. Now, the price of good1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compensating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (c) What is amount of the equivalent variation? How to interpret it?
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT