If the Utility function of an individual takes the form u(x, y) = (x + 2)² (y + 3)³ where U is total utility, and x and y are the quantities of two commodities consumed. what is the value of marginal utility of x ( or u) when x =2 and y = 1? 436 512 543 625
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- Solve; a consumer utility function is given as 64q10.5q20.25q30.4 1. what is the marginal utility of consuming commodities q1, q2 and q3 2. derive the second-order partial derivatives of the utility function with respect to the three pairs of commodities 3. show the cross partial derivatives with respect to q1 4.what is her total utility when q1 is 24, q2 is 30, and q3 is 15An individual utility function is given by U(x,y) = x·y. Derive this individual indirect utility function. Using this individual indirect utility function, compute her level of utility when I = $800, px = $20 and py = $40. It is equal to?If 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.
- When utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find utility level consumer gains?Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’s satisfaction. If price of Banana is increased by $.25, what will be the new combination of A and B that would maximize her utility? Show graphically and drive the demand curve for Bananasgiven the utility function U=150X+40X2-X3, derive average and marginal utility functions, Find the value of X at which total utility is maximum, and the value of X at which average utility is maximum?
- Let u(x) be a utility function that represents % and let f(.) be a continuousmonotonic function. f(x) is monotonic when x > y ⇐⇒ f(x) > f(y) a) Show that any monotonic transformation of the utility function (f ◦u) can also represent the same preferences.Suppose that a consumer has a choicebetween two goods, X and Y. If the price of X is $2 and the priceof Y is $3, how much of X and Y does the consumer purchaseper period, given an income of $17 per period? Use the followinginformation about marginal utility:Units MUX MUY1 10 52 8 43 2 34 2 25 1 2Reid has the following utility function. U = 24m1/3d1/2 where U is Reid's total utility, m is the quantity of muffin consumed, and d is the quantity of doughnuts consumed. Reid has a budget of $25.00, the price of a muffin is $1.00 and the price of doughnut is $0.60. a. What is the equation for the marginal utility Reid receives from muffins? What is the equation for the marginal utility Reid receives from doughnuts? b. What is the equation for the marginal rate of substitution, MRSm,d? Is Reid's utility function subject to the law of the diminishing marginal rate of substitution? c. Reid has a $15.00 gift card that can only be used to buy doughnuts and $10.00 cash to spend on either of the two goods. The price of a doughnut is $0.60 and the price of a muffin is $1.00. Using equations, determine, determine Reid's optimal combination of muffins and doughnuts given the cash and gift card.
- Total utility (utils) 0 80 120 148 160 155 Quantity consumed per day 0 1 2 3 4 5 As shown in Exhibit above, the marginal utility for the second unit consumed isQ12. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F.Suppose as Case X, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $15, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space.Utility functions of a consumer: U = 20x10.4x20.4 Specify:a. marginal utility of each item.b. If the consumption of x1seee is 80 and x2 as much as 60 units, the price of Px120 and Px2 25, Determine if there is a balance of consumption?