Chizzy’s has a utility function U(x1,x2) = x1x2. He originally faces the prices ($1,$1) and has...

Chizzy’s has a utility function U(x_1,x₂) = x₁x_2. He originally faces the prices ($1,$1) and has income $50. If the price of good 1 falls $0.5. What is the change in consumer surplus, compensating and equivalent variation?

Expert Solution

Rahul Sunny answered 2 years ago

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...

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...

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...

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...

Chapters 8. Slutsky Equation 1. Consider the utility function u(x1, x2) = x1x2. Suppose that the...

Chapters 8. Slutsky Equation 1. Consider the utility function u(x1, x2) = x1x2. Suppose that the prices are given 1 for each good and the income is 10. (1) Find out the optimal choice(s). Figure out the utility level at this optimal choice. (2) Suppose now that the price of good 2 increases from 1 to 2. Figure out the value of the bundle that you obtained in (1) under the new prices. Draw the budget set associated with this...

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?

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.

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...

(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...

Question