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Section A Question 1 (a) For an inferior good, decompose the effect of a price rise...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow is p2. John gets an income of m, today and m2 tomorrow. (a) John also faces the interest rate, r. Write out John's intertemporal budget constraint in present value and future forms. (4 marks) (b) It turns out that John earns an income of £15000 today and...
John consumes two goods, X and Y and has an income of $25. Price of good X is S3 per unit and price of good Y is $2 per...
John consumes two goods, X and Y and has an income of $25. Price of good X is S3 per unit and price of good Y is $2 per unit. John's utility function is given by U (X, Y) = 0.5 XY. The marginal utility of X, MUx 0.5Y and the marginal utility of Y, MUy 0.5X. (a) Determine the optimal values of X and Y that will maximize John's utility. (7 marks) (b) Calculate the total utility at the...
2) Suppose that the price of good X is $2 and the price of good Y...
2) Suppose that the price of good X is $2 and the price of good Y is $3. You have $90 to spend and your preferences over X and Y are defined as: U(x,y) = x2/3y1/3 Keep in mind that we review this concept because consumer choice is based on their preferences. People demand items that fulfill their Utility (perhaps happiness). As a result, we need to visualize how an individual’s budget is allocated to create the highest level...
1. (a) Outline the income and substitution effect of a price rise for an inferior good....
1. (a) Outline the income and substitution effect of a price rise for an inferior good. Under what circumstances will the demand curve slope downwards for an inferior good. Illustrate using a diagram. (b) (c) Bob views apples and oranges as perfect substitutes in his consumption, and MRS 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function:...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function: U (X, Y) = X°.270.3 Budget Constraint: I = XP, + YP, a. What is the consumer's marginal utility for X and for Y? b. Suppose the price of X is equal to 4 and the price of Y equal to 6. What is the utility maximizing proportion of X and Y in his consumption? {construct the budget constraint) c. If the total amount...
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a...
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a Budget Constraint = Marginal Utility of good x/Price of good x = Marginal Utility of good y/Price of y Calculate Consumption Bundle using the following information: Price of Good x = $5, Price of Good y = $16 and Income = $100 / 0 Quantity Consumed Total Utility Quantity Consumed Total Utility Calculate: a.) Price Elasticity of Demand =% Change in Quantity Demanded/%Change in...
Question 4. Laura is deciding how much to consume in periods o, 1 and 2. Suppose Laura income in period o is o, her...
Question 4. Laura is deciding how much to consume in periods o, 1 and 2. Suppose Laura income in period o is o, her income in period is y, and her income in period alsay. The price of consumption in period / is p. Assuming the interest rate is T, and consumption in period is denoted. In the utility maximization problem what variables are endogenous and which are exogenous ? Figure 1. Consider the following diagram of an indifference curve...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
QUESTION 13 Quantity Per Week Total Utility Brook Kate Amy 100 5.0 9.9 147 190 no...
QUESTION 13 Quantity Per Week Total Utility Brook Kate Amy 100 5.0 9.9 147 190 no GN- 400 450 600 1200 1800 2400 3000 3600 4200 4800 5400 32.9 425 575 900 1275 1770 372 520 510 Refer to the above table. Brook's utility schedule shows initially decreasing marginal utility and then increasing marginal utility. increasing marginal utility throughout her entire schedule. Initially increasing marginal utility and then decreasing marginal utility. diminishing marginal utility throughout her entire schedule. QUESTION 14...
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...
Question 3 John has the utility function is u(ci,C2) -c2, where c, is consumption today and c2 is consumption tomorrow. The price of consumption today is £1 and the price of consumption tomorrow is p2. John gets an income of m, today and m2 tomorrow. (a) John also faces the interest rate, r. Write out John's intertemporal budget constraint in present value and future forms. (4 marks) (b) It turns out that John earns an income of £15000 today and...
John consumes two goods, X and Y and has an income of $25. Price of good X is S3 per unit and price of good Y is $2 per unit. John's utility function is given by U (X, Y) = 0.5 XY. The marginal utility of X, MUx 0.5Y and the marginal utility of Y, MUy 0.5X. (a) Determine the optimal values of X and Y that will maximize John's utility. (7 marks) (b) Calculate the total utility at the...
1. (a) Outline the income and substitution effect of a price rise for an inferior good. Under what circumstances will the demand curve slope downwards for an inferior good. Illustrate using a diagram. (b) (c) Bob views apples and oranges as perfect substitutes in his consumption, and MRS 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function: U (X, Y) = X°.270.3 Budget Constraint: I = XP, + YP, a. What is the consumer's marginal utility for X and for Y? b. Suppose the price of X is equal to 4 and the price of Y equal to 6. What is the utility maximizing proportion of X and Y in his consumption? {construct the budget constraint) c. If the total amount...
Optimal Consumption of good x and good y: Maximization Rule - Maximization of Utility given a Budget Constraint = Marginal Utility of good x/Price of good x = Marginal Utility of good y/Price of y Calculate Consumption Bundle using the following information: Price of Good x = $5, Price of Good y = $16 and Income = $100 / 0 Quantity Consumed Total Utility Quantity Consumed Total Utility Calculate: a.) Price Elasticity of Demand =% Change in Quantity Demanded/%Change in...
Question 4. Laura is deciding how much to consume in periods o, 1 and 2. Suppose Laura income in period o is o, her income in period is y, and her income in period alsay. The price of consumption in period / is p. Assuming the interest rate is T, and consumption in period is denoted. In the utility maximization problem what variables are endogenous and which are exogenous ? Figure 1. Consider the following diagram of an indifference curve...
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
QUESTION 13 Quantity Per Week Total Utility Brook Kate Amy 100 5.0 9.9 147 190 no GN- 400 450 600 1200 1800 2400 3000 3600 4200 4800 5400 32.9 425 575 900 1275 1770 372 520 510 Refer to the above table. Brook's utility schedule shows initially decreasing marginal utility and then increasing marginal utility. increasing marginal utility throughout her entire schedule. Initially increasing marginal utility and then decreasing marginal utility. diminishing marginal utility throughout her entire schedule. QUESTION 14...
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...
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