Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6. Derive the Marshallian demand functions for ?1 and ?2 as functions of both prices and income. Then find the optimal consumption point for the given budget constraint.
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Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) .
She spends her budget of £27 for two goods.
The prices of both goods are p1 = 6 and p2 = 6.
Derive the Marshallian demand functions for ?1 and ?2 as functions of both prices and income. Then find the optimal consumption point for the given budget constraint.
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- Let a1 and x2 denote the quantities consumed. The consumer's preferences are represented by the utility function: U (r1, 22) = V+ VT2. Suppose the consumer has income m =100 and that the prices for the two goods are pi -2 and p2=8. Calculate the optimal quantity demanded for good 1.Consider the following utility function: U = 100x°.50,0.50 A consumer faces prices of P, = $2 and P, =$1 Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. 15 stv МacВook Air 80 DI esc F1 F2 F3 F4 F5 F6 F7 F8 @ %23 2$ & 1 2 4 6 7 8 Q W T Y tab A S F H J K aps lock C V M control option command B HIf the price for good x1 is p1 = 2, the price for good x2 is p2 = 3, and Kramer’s available income is m = 16, write down Kramer’s budget constraint. Using the prices and income given at (b) above, find Kramer’s optimal consumption choice (Marshallian demand) and his corresponding utility level.
- Suppose that i's preferences over goods x and y are represented by the following utility function U₁(x, y)=x45¹5. Let m denote the consumer's income, p denote the price of good x and let the price of good y equal 1. A) Find the Marshallian demand functions for goods x and y. B) Show how each of the demand function is affected by a change in the price of good x. C) Which of the goods is an inferior good?Rui's utility function is Let the price of good X be px, the price of good Z be normalized to $1.00, and U be her level of well-being. What is her expenditure function? Rui's expenditure function (E) is E = 2. U=X+4XZ+Z. PX(U+0.25) 2 - 0.25 (Px +1) · (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the _ character.) Derive her unco pensated demand curve for X. Let Y be her income. Rui's uncompensated demand curve for good X is (Properly format your expression using the tools in the palette.) X=(b) U(x, y) = min [ax, y]
- Consider a consumer who consumes pizzas and soft drinks. The utility function is given by U(p, s) = pa 8B, where p represents the quantity of pizzas consumed and S represents the quantity of soft drinks consumed, and a and Bare positive constants representing the consumer's preferences for each good. Assume a = 2 and ẞ = 1. If the prices of pizzas and soft drinks are $10 and $2 respectively, and the consumer has $50 to spend, which of the following statements is wrong? The slope of the budget constraint indicates that for every extra soda drink the consumer buys, they must give up 5 pizzas. The slope of the budget constraint indicates that for every extra pizza that the consumer buys, they must give up 5 soda drinks. If this consumer buys O soda drinks, their total utility will be 0. If this consumer buys 1 pizza, their consumption of soda drinks will be 20.Joyce drinks both coffee (x) and tea (y). Her preferences over these two goods can be represented by the utility function U(x,y) =x + 3y^1/2 where x represents the number of pounds of coffee and y represents the number of cups of tea. a) Given her preferences, find her demand functions for coffee (x) and tea (y). b) Suppose that the price of a pound of coffee is $4 and that she has $56 to spend on coffee and tea. Write her demand curve for tea. Illustrate her demand curve. c) Suppose that the price of a cup of tea is $1 (the price of coffee and income remain $4 and $56, resp.). Use your demand functions to find her best bundle. In an indifference curve diagram illustrate her best bundle at these prices. For the remainder of the question, assume that her income rises to $60 and that the prices of coffee and tea are unchanged at = $4 and =1.Suppose that i’s preferences over goods x and y are represented by the following utility function Ui(x, y)=x^0.8·y^0.2. Let m denote the consumer’s income, p denote the price of good x and let the price of good y equal 1. a) Find the Marshallian demand functions for goods x and y. b) Show how each of the demand function is affected by a change in the price of good x. c) Which of the goods is an inferior good?
- A consumer has preferences over two goods, denominated by x and y, given by the utility function U(x,y) = min{αx,y} with α > 0. The prices of the good are px = 2 and py = 5. The consumer has an income of I > 0. (a) Provide an intuition for this utility function. Specifically, are these goods substitutes or complements? If x is bicycle tires and y is bicycle frames, what is the value for α? (b) For what values of α will the consumer demand (i.e., Walrasian demand) more x than y. (c) For what values of α will the consumer spend more on x than on y (given her Walrasian demands).Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6 Now suppose that instead both goods are priced as follows: There is a discount of 50% on the price of good 1 on each additional unit in excess of 3 units, and there is a discount of 50% on the price of good 2 on each additional unit in excess of 3 units. Draw the new budget constraint and derive it analytically.Suppose that an individual consumes two goods X and Y, and his direct utility function is given by: U(X, Y) = X" + Y"s. a) Derive the Marshallian demand functions for X. b) Derive the Marshallian income elasticity of good X.