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Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m. 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods. For each of your answers in question 2, write down the consumer...
Solve Problem 2 1. A consumer maximizes his utility function, 122, subject to the budget constraint,...
Solve Problem 2
1. A consumer maximizes his utility function, 122, subject to the budget constraint, 75x1 +150x2-525· (M-$75, P2-$150, M-$525). Set up the Lagrangian function and use the first-order and second-order conditions to find the values of x1 and x2 that solve the consumer's problem 2. This problem is an extension of Problem 1. Now, the consumer faces an additional constraint. Specifically, good 1 is rationed, and the consumer can buy no more than three units of that good....
Question 4: Consider a general utility function U(xi, x2). Let's now solve for the optimal bundle...
Question 4: Consider a general utility function U(xi, x2). Let's now solve for the optimal bundle generally using the Lagrangian Method. 1. Write down the objective function and constraint in math 2. Set up the Lagrangian Equation 3. Fnd the first derivatives. 4, Find the first order conditions, what's the interpretation for λ? 5. Rearrange them to get the tangency condition.
1. Price of x is 12 and price of y is 8. Answer the following questions...
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
Each firm produces both goods, i.e., good 1 and good 2. Each firm takes the market prices p 0 and p2 2 0 as firm produc...
Each firm produces both goods, i.e., good 1 and good 2. Each firm takes the market prices p 0 and p2 2 0 as firm produces T units of good 1 and x2 units of good 2, with (xi, x2) the total costs of C(x.x) = 2i+0.5«% given and chooses output to maximize profits.1 If a R2, it has 1200 (a) (1 point ) For given prices p1 and p2, find the revenue, R(x1, x2), of a single firm (b)...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py...
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...
can anyone help me with this question? 2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consum...
can
anyone help me with this question?
2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m. 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods. For each of your answers in question 2, write down the consumer...
Solve Problem 2
1. A consumer maximizes his utility function, 122, subject to the budget constraint, 75x1 +150x2-525· (M-$75, P2-$150, M-$525). Set up the Lagrangian function and use the first-order and second-order conditions to find the values of x1 and x2 that solve the consumer's problem 2. This problem is an extension of Problem 1. Now, the consumer faces an additional constraint. Specifically, good 1 is rationed, and the consumer can buy no more than three units of that good....
Question 4: Consider a general utility function U(xi, x2). Let's now solve for the optimal bundle generally using the Lagrangian Method. 1. Write down the objective function and constraint in math 2. Set up the Lagrangian Equation 3. Fnd the first derivatives. 4, Find the first order conditions, what's the interpretation for λ? 5. Rearrange them to get the tangency condition.
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
Each firm produces both goods, i.e., good 1 and good 2. Each firm takes the market prices p 0 and p2 2 0 as firm produces T units of good 1 and x2 units of good 2, with (xi, x2) the total costs of C(x.x) = 2i+0.5«% given and chooses output to maximize profits.1 If a R2, it has 1200 (a) (1 point ) For given prices p1 and p2, find the revenue, R(x1, x2), of a single firm (b)...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
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...
can
anyone help me with this question?
2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0 where c1 and c2 are consumption in period 1 and period 2 respectively (Portfolio Choice Problem) Now suppose that the consumer can save in terms of two instruments: financial savings (s) and capital investment (k). Capital investment done in period 1 yields output ka with 0 < α < 1 in period 2....
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
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