Separately, draw the indifference curves that cross through the bundles (1, 1) and (4,4) for the following preference ii) U(x1, x2) = max{2x1+y, 2x2 + ¤1} Aro th oce proforo ncos c onvox2
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- 10. Consider the utility function U(x, y) = xy + x. Which of the following bundles is noton the same indifference curves as the others. Note: The first entry is the amount of x, thesecond is the amount of y.(a) (5,1)(b) (2,4)(c) (4,2)(d) (2.5,3)Depart from the represented preferences U(x,y)= min {x, 4y} 1. Draw two indifference curves for the given utility function and show the preferred points, by providing examples. 2. Explain mathematically the MRS for the different parts of this type of IC.Given the budget line and indifference curvesshown in Exhibit A-6, assume the consumer isinitially at point C. To maximize total utility, theconsumer shoulda. purchase more of good X and less of good Y.b. remain at point C.c. move to point B and then to point A.d. purchase more of good Y and less of good X.
- Assume an individual’s preference for Fanta (Good x) and Fritters (Good y) are given by the following utility function: U(x,y)=20= x^0.5y^0.5 REQUIRED: i) Derive the equation for the indifference curve for this utility functionGiven that utility function for a consumer is given by u = (x-3)2 + (y-4)2, draw any twoindifference curves for this consumer while clearly labelling the higher one as ‘H’ and lower oneas ‘L’. Does he prefer more of a good to less of it? Does he prefer averages to extremebundles? Explain.Suppose a consumer buys only two goods x and y and spends her entire income on these teo goods. She must first but some fixed quantity y before she buys any amount of x. After purchasing y; what matters is the quantity of x only and utility will increase only by buying more x. Please Draw the indifference curves. * Please draw the indifference curves as the solution*
- Gopal is a rational consumer and consumes two goods X and Y. Is a cardinal measureof utility or satisfaction necessary in order to sketch a set of indifference curves? Whatare the main characteristics of indifference curves? On the same set of axis draw threeindifference curves showing increasing marginal rate of substitution as we move downthe indifference curve. Please answer it in little more detail as it is descriptiveSuppose an individual has the following utility function: U(x,y)=−4(x−5.5)^2 −2(y−3.5)^2 Further assume that the price of good x, px = $6, the price of good y, py = $8 and the individual has an income m = $65 a) Draw an indifference curve (one IC is enough) that represents this person’s prefer- ences. Please label the graph properly including values for x and y. b) Intuitively, and without formally solving, can you guess the maximized values x* and y*for the above utility function. Explain your answer. c) Derive the optimal values x*and y*by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class. d) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers you found in parts b) and c) (if any). Be as detailed as possible with your explanation.ASAP 1. Consider a consumer with utility u(x1,x2) = .5lnx1 + .5lnx2 (b) Now, consider an equivalent representation of the above utility functionx51 x52 Does this utility function have the "increasing difference property"? Howabout the "strict increasing difference" property?
- Q4 please help fast all info is there! Rachel has the utility function U(xA.×B) = xAxB where xa is the number of apples, and xBis the number of bananas. Her indifference curve passing through 12 apples and 4 bananas will also pass through the point where she consumes 6 apples and O 6 bananas. O 4 bananas. O 8 bananas. O 12 bananas.Graph and explain indifference curves for the following situations:(i) An individual has constant marginal utility toconsumption in both periods.(ii) An individual does not derive utility from this period’sconsumption, but does from the next period’sconsumption.(iii) An individual’s utility decreases with consumption inboth periods.Suppose an individual has a utility function u (x1, x2) = 2*2. Present your mathmatical expressions below in the simplest form you can. a) Derive an expression for the marginal utility of good 1, and for the marginal utility of good 2. b) Using these, solve for an expression describing the slope of an indifference curve: MRS (11, 12). c) Sketch indifference curves for this consumer corresponding to u = 0,10,20. (Hint: z rı = k solves for m} = 11 (21) . Solve this expression and approximate it on a graph for the three values of k.)
