Intuition. Consider this problem.
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Intuition. Consider this problem.
ma U = x + y e need to relax the usual...
a) ANSWER : Only good y is consumed. Optimal consumption of X= 0 . Optimal consumption...
a) ANSWER : Only good y is consumed. Optimal consumption
of X= 0 . Optimal consumption of Y= I/Py
b) ANSWER: only good x is consumed. Optimal consumption
of X= I/Px . Optimal consumption of Y = 0
only answer C.
4. (16 points) Intuition. Consider this problem. We need to relax the usual two conditions we assume for an optimal solution (tangency and binding constraint) because this problem will yield corner solutions. a) (6 points) Suppose Px 1 and...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B)...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find X* and Y*.
U 1 3 x 3 y 4 = Suppose the price of x is given by...
U 1 3 x 3 y 4 = Suppose the price of x is given by px and the price of y is given by Py and the budget income of the consumer is given by 1. Price of x, Price of y and Income are always strictly positive. Assume interior solution. a) Write the statement of the problem (1 point) b) Compute the parametric expressions of the equilibrium quantity of x & y purchased and the maximized utility. You...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find X* and Y*.
Consider preferences over x and y given U(x,y) = min(x,2y) and suppose that income is 60....
Consider preferences over x and y given U(x,y) = min(x,2y) and suppose that income is 60. Let the initial prices be px=1 and py=2. 1. What is the initial optimal consumption? 2. Suppose px increases to px=2. Find the total change in the consumption of x and y. 3. Decompose the total effect into its substitution effect and its income effect. Please do each step of every question for a complete understanding of the reasoning behind the steps.
Your friend has the following utility unction: U(X,Y) = 10 X + 40 Y – X2-...
Your friend has the following utility unction: U(X,Y) = 10 X + 40 Y – X2- 3Y2 Where X is her consumption of Redbox movies, with price Px = $1, and Y is her consumption of iTunes, with Py = $2. Income is 48 dollars. a. Using the Lagrangian approach, derive your friend’s demand equations for Redbox movies and iTunes. That is, find X and Y. (Hint: Substitute the budget constraint in the Lagrangian problem using the given prices and...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4)...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
Suppose that a consumer’s utility function is U(x,y)=xy＋10y. the marginal utilities for this utility function are...
Suppose that a consumer’s utility function is U(x,y)=xy＋10y. the marginal utilities for this utility function are MUx=y and MUy=x＋10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
1. Suppose a consumer has the utility function over goods x and y u(x, y) =...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
a) ANSWER : Only good y is consumed. Optimal consumption
of X= 0 . Optimal consumption of Y= I/Py
b) ANSWER: only good x is consumed. Optimal consumption
of X= I/Px . Optimal consumption of Y = 0
only answer C.
4. (16 points) Intuition. Consider this problem. We need to relax the usual two conditions we assume for an optimal solution (tangency and binding constraint) because this problem will yield corner solutions. a) (6 points) Suppose Px 1 and...
U 1 3 x 3 y 4 = Suppose the price of x is given by px and the price of y is given by Py and the budget income of the consumer is given by 1. Price of x, Price of y and Income are always strictly positive. Assume interior solution. a) Write the statement of the problem (1 point) b) Compute the parametric expressions of the equilibrium quantity of x & y purchased and the maximized utility. You...
1. Suppose a consumer has the utility function over goods x and y u(x, y) = 3x}}} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x (Px, py,m) and y* (Px, Py,m). Show all of your work and circle your final...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x3 yž (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px, Py,m) and y* (Px, Py,m). Show all of your work and circle your final...
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