1. ?(?, ?) = ? ?^? ?^? A) Find out the optimal demand of good m...
1. ?(?, ?) = ? ?^? ?^?
A) Find out the optimal demand of good m and n in terms of prices, r, s, and w. b)Write down the Lagrangian for the utility optimization problem
Homework Answers
question #6 P2 = $1 for each Gala. Find her optimal demand and show it on...
question #6
P2 = $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand For each of the following utility functions, write down a transformation that would turn it into a Cobb-Douglas utility function of the form U(, )"ys where a B-1. (a) U(x, y) γχαν'-a where γ is a constant. (b) U(, y)-y 6. For each of the following utility functions, write down 2 monotonic...
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...
d. U (1, ) (1a)(b-a For the utility function above, find the consumer's optimal consumption bundle...
d. U (1, ) (1a)(b-a 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...
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...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect utility function v(p, w). (b) Find the Hicksian demand function h(p, u) and the expenditure function e(p, u). (c) For the remainder of the problem, suppose α = 4 and w = 5. If p = (2,1), what is5 the optimal bundle? What is the utility of that bundle? [Leave your answer in terms of fractions and exponents] (d) Suppose the price of good...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect...
Suppose u(x1, x2 ) = x1^ax2^1-a (a) Find the optimal bundle x(p, w) and the indirect utility function v(p, w). (b) Find the Hicksian demand function h(p, u) and the expenditure function e(p, u). (c) For the remainder of the problem, suppose α = 4 and w = 5. If p = (2,1), what is5 the optimal bundle? What is the utility of that bundle? [Leave your answer in terms of fractions and exponents] (d) Suppose the price of good...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his...
2*. Assume that Bob has a budget constraint p1x1 + p2x2 = m, and that his preferences are represented by the Cobb-Douglas utility function U(x1, x2) = x1 c x2 d , where c>0 and d>0. State Bob’s optimization (utility maximization) problem. a) Set up the Lagrangian function. b) Derive the necessary conditions (the first-order conditions) for an optimal interior solution. c) Show that the MRS (the slope of the indifference curve) is equal to the slope of the budget...
question #6
P2 = $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand For each of the following utility functions, write down a transformation that would turn it into a Cobb-Douglas utility function of the form U(, )"ys where a B-1. (a) U(x, y) γχαν'-a where γ is a constant. (b) U(, y)-y 6. For each of the following utility functions, write down 2 monotonic...
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...
d. U (1, ) (1a)(b-a 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...
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...
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
A monopolist has a production function 27 (L-2)(K+1) Q(L,K) where L, Kis the amount of labor and capital. The wage rate is denoted by w and the rental rate of capital is denoted by r. The inverse demand function the monopolist is faced with is given by P = 12- 3Q where P is the market price and Q is the quantity sold. 13. Write down the optimization problem of the monopolist. 14. Write down the first order condition(s) 15....
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