2. The prices are (P1, P2) = (2,3), and the consumer is currently consuming (x1, x2) = (4, 4). (a) Will the consumer necessarily prefer to consume the bundle (x1, x2) = (3,5) over the bundle (x1, x2) = (4,4). Why? (b) Will the consumer necessarily prefer to have the bundle (x1, x2) = (3, 5) over the bundle (x1, x2) = (4,4). Why?
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- 2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) = (15,20). The monthly budget is: M = 600, answer the following:a. What is the optimal bundle (X, Y) that maximizes the consumer’s utility?b. What is the optimal utility given your answer from part a?c. If the desired level of utility the consumer is U = 400, what would be the optimal bundle (X, Y) to minimize consumer expenses?d. Given U = 400 from part c, what would be the new optimal bundle for both goods if PX increases to 25?e. Given the price increase in good X from part d, what would be the optimal bundle for this consumer wishing to maximize its utility with an income, M = 600?f.: Graph the budget line and utility curve from part a.2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) = (15,20). The monthly budget is: M = 600, answer the following:a. What is the optimal bundle (X, Y) that maximizes the consumer’s utility?b. What is the optimal utility given your answer from part a?c. If the desired level of utility the consumer is U = 400, what would be the optimal bundle (X, Y) to minimize consumer expenses?d. Given U = 400 from part c, what would be the new optimal bundle for both goods if PX increases to 25?e. Given the price increase in good X from part d, what would be the optimal bundle for this consumer wishing to maximize its utility with an income, M = 600?f.: Graph the budget line and utility curve from part a i need help on part cIf the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.
- Q: A consumer’s preferences for food (F) and clothing (C) are given by U(F,C) = F0.2C0.8. The price of food is $4, and the price of clothing is $8. The consumer has an income of $3600. a) What is the utility maximizing choice of food and clothing? b) How would the utility maximizing choice change if price of clothing increased to $14? c) Given the answers to the previous parts plot a linear approximation to the demand function for clothing.Question 7 You are currently at the bundle (x, y) = (4, 2) with a utility function U = In(x) + In(y). I offer you one additional unit of x for 2 units of y. Do you make the trade with me? Explain.A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility yielded by their consumption is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. (a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. (b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z? Product X Product Y Quantity Utility Marginal Quantity Utility Marginal Utility Utility per$ per$ 1 23 4567 42 82 118 148 170 182 182 1 23 4 5 6 7 14 26 36 44 50 54 56.4 Product Z Quantity Utility Marginal Utility per$ 1 23456 7 32 60 84 100 110 116 120 3..
- 21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂
- 1. For each of the following three utility functions below, find the demand function by explicitly solving each utility maximization problem. (a) u(x1,x2) = xx. (b) u(x1, x2) = Inx1+2lnx2. (c) u(x1,x2) = x7x3.2. Maria likes to have one cup of coffee (x) and two slices of bread (y) each morning. Which of the following utility functions represents Maria's preference for (x, y)? (a) U(x, y) = min(8x, 2y) (b) U(x, y) = min (4x, 2y) - RIGHT ANSWER (c) U(x, y) = min(x, 2y) (d) U(x, y) = min(x, 2y)1. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are px and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. = (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px = 10, Py = 5 and m = 100. Suppose that px increases to p how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y > 0). = 15,
