Question

In: Economics

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 effect on the demand of x1

and explain how is it different from the hicks substitution effect.

Solutions

Expert Solution


Related Solutions

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...
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.
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...
(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...
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.
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(x1,x2) = x1x2. 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?
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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT