Given the utility function u(x1, x2) = max{lnx1, lnx2}. What is the consumer's demand function for...

Given the utility function u(x1, x2) = max{lnx₁, lnx₂}. What is the consumer's demand function for good 1? And the indirect utility function, expenditure function.

Expert Solution

Rahul Sunny answered 1 year ago

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....

Given the utility function U(x1, x2)= -2x1 + x2^2, (a)Find the marginal utility of both the...

Given the utility function U(x1, x2)= -2x1 + x2^2, (a)Find the marginal utility of both the goods. Explain whether preferences satisfy monotonicity in both goods. (b)Using the graph with a reference bundle A, draw the indifference curve and shade the quadrants that make the consumer worse off and better off for the given preferences.

(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...

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...

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?

Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent...

Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent the two goods Sophie consumes. Sophie's income is $3400 and the prices are given as x1 = $2 and x2 = $160 a) derive & represent in two separate diagrams the demand for x1 and x2 ( for any income and prices) b) If Sophie's income is increased to $6600, what is the income effect on x1? Is x2 a normal good? Justify your...

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...

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