What is the logarithmic transform of the utility function U=xα1xβ2xγ3 given the budget constraint px1x1+px2x2+px3x3=M . Select one: a. ln U=ln xα1+ln xβ2+ln xγ3 b. ln U=ln xγ1+ln xβ2+ln xα3 c. ln U=α ln x1−β ln x2−γ ln x3 d. ln U=α ln x1+β ln x2+γ ln x3
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What is the logarithmic transform of the utility function U=xα1xβ2xγ3 given the budget constraint px1x1+px2x2+px3x3=M
.
ln U=ln xα1+ln xβ2+ln xγ3
ln U=ln xγ1+ln xβ2+ln xα3
ln U=α ln x1−β ln x2−γ ln x3
ln U=α ln x1+β ln x2+γ ln x3
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- What is the logarithmic transform of the utility function U=xα1xβ2xγ3U=x1αx2βx3γ given the budget constraint px1x1+px2x2+px3x3=Mpx1x1+px2x2+px3x3=M. Select one: a. ln U=ln xα1+ln xβ2+ln xγ3ln U=ln x1α+ln x2β+ln x3γ b. ln U=α ln x1−β ln x2−γ ln x3ln U=α ln x1−β ln x2−γ ln x3 c. ln U=α ln x1+β ln x2+γ ln x3ln U=α ln x1+β ln x2+γ ln x3 d. ln U=ln xγ1+ln xβ2+ln xα3Which of the FF. statements is correct regarding the preference of the consumers when the income of the consumer can only be spent between apples and oranges? Assume that apples are written on the vertical axis while oranges are written on the horizontal axis A. when the consumer has few oranges, he is willing to trade more apple to get another orange B. when the consumer has so many oranges already, he will only exchange less apples for an orange C. the declining slope of the indifference curve shows the marginal value of oranges is declining D. all are correct E. none is correctFor the following utility function find the MRS at (x, y) = (2, 3) a) U(x, y) =2x +y b) U(x, y) =x^3 y^2 c) U(x, y) =min(x, 2y) Solve subparts (c )correctly
- Utility Function: U(X,Y)=X1/2Y1/2 Budget Constraint: 2X+2Y=16 If the price of good X changes to Px=3, what is the Equivalent variation?what is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPiisuppose a consumer consumes two goods x and y with utility function u=x^0.5+y^1.5, does the utility funciton exhibit diminishing marginal utility for (i) x (ii)y?
- Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.Draw a budget constraint for an individual where if all income is dedicated to consumption of good X, the consumer can consume 40 units, and similarly, if the consumer dedicates all income to good Y 40 units can be consumed. What is the slope of the budget constraint? Draw in an indifference curve for this consumer showing an initial consumer equilibrium, with consumption of X and Y labelled. Now suppose that the price of good X falls such that 80 units of X could be purchased if the consumer dedicates all income to good X. What is the price ratio and slope of the new budget constraint? Draw in a new indifference curve tangent to the new budget constraint, together with consumption of X and Y. Identify the income and substitution effects graphically.For the utility function U = Qx0.46Qy(1-0.46) and the budget 100 = 11Qx + 11Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.5. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
- John has preferences for food F and clothing C described by a utility function . Suppose that food costs $1 a unit and that clothing costs $2 a unit. John has $12 to spend on food and clothing. On a graph, draw indifference curves corresponding to , , . Make sure to label coordinates clearly. Using the graph, find the optimal choice of food and clothing. Let the amount of food be on the horizontal axis and the amount of clothing be on the vertical axis. What is the marginal rate of substitution of food for clothing at his optimal basket? Show this graphically and algebraically. Suppose John decides to buy 4 units of food and 4 units of clothing with his $12 budget. Would his marginal utility per dollar spent on food be greater than or less than his marginal utility per dollar spent on clothing? What does this tell you about how he should substitute food for clothing if he wanted to increase his utility without spending any more money?A consumer utility function is U=(x1,x2) Where X1 is the quantity of good 1 that is bought, X2 is the quantity of good 2 that is bought. The price of good 1 is $10 and the price for good 2 is $2. If the consumer's income is $100 what will the consumer's optimal utility level be? b. Using Lagrange multilplier method. optimise the utility function x0.25 y0.25 subject to the budget constraint 24=x/10+yAssume a consumer has a utility function U(x1, x2) = x1x2 where x1, x2 represents the amount of two goods 1 and 2 consumed in a given time period, find the utility-maximizing consumption function subject to the budget constraint5x1 + 4x2 <= 50