Consider a household utility U = In(X)
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4. Let the household utility function be given by U(x,y) = Vxy. a. Find the marginal...
4. Let the household utility function be given by U(x,y) = Vxy. a. Find the marginal utilities of X and Y and write the expression for the marginal rate of substitution between X and Y. b. Let I = $100, Px = $10 and Ry = $10 be the set of prices and income. Find the utility maximizing combination of X and Y given the prices and income. c. What is the level of utility of the chosen bundle of...
Question 2 2 pts Consider the utility function u(x1, x2)= x x Calculate the marginal utility...
Question 2 2 pts Consider the utility function u(x1, x2)= x x Calculate the marginal utility of good 2. 7xx? O 7xx? 7x x 8xx
3. Assume that a household has the following utility function: U = 100q1 +242 a) (10...
3. Assume that a household has the following utility function: U = 100q1 +242 a) (10 points) Suppose the household has an income of Y - $800, and a per unit price of food pi $5 and price of clothing p2 - $0.1. What is the utility- maximizing bundle? b) (5 points) Suppose the price of the first good increases to $6 per unit. What is the utility maximizing bundle?
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that...
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
Consider the utility function of an individual given by u(x) - ln(x - 10, 000). His...
Consider the utility function of an individual given by u(x) - ln(x - 10, 000). His total wealth is $270,000 of which S170,000 is the worth of his house. There is 10% probability that his house may be destroyed by fire. (a) What is the risk attitude of this person? (10%) (b) Calculate the insurance premium. fair premium and risk premium. (1596) (c) What is the relationship between the insurance premium, fair premium, and 2.
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
1. Consider an agent with preferences represented by the utility function: u(x,y) = xy (a) For...
1. Consider an agent with preferences represented by the utility function: u(x,y) = xy (a) For each pair of bundles, indicate which is preferred or if they are indifferent between the two. Show your work. (4 points) A (3,9) B(2,8) ------------ C(4,7) D(8,8) E (5,20) F(10,10) G(5,9) H(12,4) (b) Using the bundles in (a), make a list that orders the bundles according to the agent's preferences. Start the descending list with the most preferred bundle and end with the least...
Consider a customer (i) with a utility function u(x, y) = 200x − 25x2 + y...
Consider a customer (i) with a utility function u(x, y) = 200x − 25x2 + y where the price of good x is $p, and the price of the composite good y is one dollar ($1). Also, assume that each consumer has an income I. (MUx=200-50x , and MUy=1) Derive the consumer's demand function for good x. Now, consider an economy with 100 exact same type of consumers. Calculate an aggregate demand for only good x. Now, consider a firm...
Suppose the representative household has the following utility function: U (C; l) = ln C +...
Suppose the representative household has the following utility function: U (C; l) = ln C + 0:5 ln l where C is consumption and l is leisure. The householdís time constraint is l+N=1 where Ns is the representative householdís labour supply. Further assume that the production function is Cobb-Douglas zK0:5 (N)0:5 where z = 1 and K = 1: 2.1 Assuming that the government spending is G = 0; use the Social Plannerís problem to solve for Pareto optimal numerical...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c)...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c) + Bln(c'), where B is a parameter between 0 and 1, and assume that there is always an interior solution to the household's problem. 12. What is the marginal rate of substitution of current consumption for future con- sumption MRS given this utility function? How does it change with c and c'? 13. Solve the household's optimization problem with the lifetime budget constraint. That...
4. Let the household utility function be given by U(x,y) = Vxy. a. Find the marginal utilities of X and Y and write the expression for the marginal rate of substitution between X and Y. b. Let I = $100, Px = $10 and Ry = $10 be the set of prices and income. Find the utility maximizing combination of X and Y given the prices and income. c. What is the level of utility of the chosen bundle of...
Question 2 2 pts Consider the utility function u(x1, x2)= x x Calculate the marginal utility of good 2. 7xx? O 7xx? 7x x 8xx
3. Assume that a household has the following utility function: U = 100q1 +242 a) (10 points) Suppose the household has an income of Y - $800, and a per unit price of food pi $5 and price of clothing p2 - $0.1. What is the utility- maximizing bundle? b) (5 points) Suppose the price of the first good increases to $6 per unit. What is the utility maximizing bundle?
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
Consider the utility function of an individual given by u(x) - ln(x - 10, 000). His total wealth is $270,000 of which S170,000 is the worth of his house. There is 10% probability that his house may be destroyed by fire. (a) What is the risk attitude of this person? (10%) (b) Calculate the insurance premium. fair premium and risk premium. (1596) (c) What is the relationship between the insurance premium, fair premium, and 2.
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
1. Consider an agent with preferences represented by the utility function: u(x,y) = xy (a) For each pair of bundles, indicate which is preferred or if they are indifferent between the two. Show your work. (4 points) A (3,9) B(2,8) ------------ C(4,7) D(8,8) E (5,20) F(10,10) G(5,9) H(12,4) (b) Using the bundles in (a), make a list that orders the bundles according to the agent's preferences. Start the descending list with the most preferred bundle and end with the least...
For Question 12 to 15, let the utility function of the household be U(c,d) = ln(c) + Bln(c'), where B is a parameter between 0 and 1, and assume that there is always an interior solution to the household's problem. 12. What is the marginal rate of substitution of current consumption for future con- sumption MRS given this utility function? How does it change with c and c'? 13. Solve the household's optimization problem with the lifetime budget constraint. That...
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