how do you solve without lagrangians?
Initial MRS=-MU/MUy= -1/(10-y)
Slope of Budget constraint= -Px/Py= -1/5
optimal bundle:
-1/5=-1/(10-y)
10-y=5
y*= 5
Budget constraint: x+5y=200
x=200-5*5=175
x*=175
U= 175+10*5-5^2/2=175+50-12.5= 212.5
When Py=1
slope of budget constraint= -1/1=-1
-1=-1/(10-y)
10-y=1
y*= 9
x+y=200
x*=200-9= 192
U= 191+10*9-9^2/2= 240.5
The maximum price Pablo will be willing to pay= 240.5-212.5=$28
So, Answer=$28
how do you solve without lagrangians? 12 Pablo's utility function is U(x,y)= x+10y- y2/2, where x...
Question (5): A consumer who has a utility function modeled as U(x,y) = min (5x, 10y) is faced with the prices of $2 and $6 per unit of x and y respectively. The consumer will spend his/her entire disposable income of $30. How many units of x and y will the consumer consume that will provide the maximum utility?! (a) 6 units of x and 3 units of y. (b) 3 units of x and 6 units of y. (c)...
Please show work: 3. Ollie has a utility function u(x, y) = (x + 2)(y + 3). The price of x is $1, and the price of y is $1. When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods. In what proportion does Ollie consume goods x and y?
How do you solve this without lagrangians? 2. Suppose that Romeo has the utility function U=SORS', and Juliet has the utility function U = S'RS,, where Sr is Romeo's spaghetti consumption and S, is Juliet's. = They have 36 units of spaghetti to divide between them. a. Romeo would want to give Juliet some spaghetti if he had more than 18 units of spaghetti. b. Juliet would want to give Romeo some spaghetti if she had more than 25 units....
1. Consumer’s utility function is: U (X,Y) = 10X + Y. Consumer’s income M is 40 euros, the price per unit of good X (i.e. Px ) is 5 euros and the price per unit of good Y (i.e. Py) is 1 euro. a) What is the marginal utility of good X (MUx) for the consumer? ( Answer: MUx = 10) b) What is the marginal utility of good Y (MUy) for the consumer? ( Answer: MUy = 1) c)...
Jon Snow consumes pizza and burgers. His utility function is u(P, B) = PB where P is the number of pizzas and B is the number of burgers. Jon Snow has $30 to spend, and he plans to spend it all on pizza and burgers. The price of one pizza is $10 and the price of one burger is $3. (a) Find and label Jon Snow’s initial optimal bundle on a graph where pizza is on the x-axis and burgers...
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
4. Malachi only consumes 2 goods: DVD rentals and coffee. His utility function is U(RC)-Rº4CO6 where R is the number of DVD rentals and C is cups of coffee. Malachi has $30 in his pocket right now, and he plans to spend all of the money on rentals and coffee today. a. The price of one rental is $3 and the price of one cup of coffee is $2 per cup. Solve for the optimal bundle. b. Suppose that Malachi...
4. Malachi only consumes 2 goods: DVD rentals and coffee. His utility function is U(R,C)=R0.4C0.6 where R is the number of DVD rentals and C is cups of coffee. Malachi has $30 in his pocket right now, and he plans to spend all of the money on rentals and coffee today. a. The price of one rental is $3 and the price of one cup of coffee is $2 per cup. Solve for the optimal bundle. b. Suppose that Malachi...
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of your budget on Chimichangas, which is totally reasonable after the Dumpling House tragedy. a) Solve the utility maximization problem, finding the uncompensated demand for x, & x, and the indirect utility function in terms of p,, p, and Y. b) Solve the expenditure minimization problem,...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...