If bundle A lies on an indifference curve ai de ) and bundle B lies above of the curve (i ), the individual: O A. prefers bundle B to bundle A B. none of the above O C. prefers bundle A to bundle B O D. enjoys bundle A and B equally
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- 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 descriptive10. 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)Suppose 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.
- (d) What point in the graph will lead to utility maximizing with the budget line LZ and the indifference curves as shown above? Please label the point C. (e) What is the marginal rate of substitution (slope of the indifference curve) at the utility maximizing point you have shown in (d)?(f) Please explain why the consumer will not choose point A or point B.Assume that an individual has convex indifference curves (i.e. diminishing MRS). Suppose the individual has $3 to spend on good #1 and good #2. In addition, suppose we know that at the bundle where q1=1 and q2=1, the marginal utility of good #1 is 2 utils and the marginal utility of good #2 is 1 util. Given this information, which set of prices would this individual prefer to face? A. p1=1 and p2=2 B. p1=2 and p2=1 C. p1=2 and p2=2Graph 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.
- C) Draw the indifference curve associated with a utility level of 36 and the indifference curve associated with a utility level of 72. Are the indifference curves bowed in toward the origin? The utility that Ann receives by consuming food F and clothing C is given by ?(?, ?) = √?? 4 + ?. Food costs N$5.00 a unit, and clothing costs N$15.00 a unit. Ann’s income is N$1850.00Suppose a consumer views two goods, X and Y, as perfect complements. Her utility function is given by U = MIN [2X, Y]. Sketch the graph of the consumers indifference curve that goes through the bundle X = 7 and Y = 8. Put the amount of Y on the vertical axis, and the amount of X on the horizontal axis. Which of the three assumptions that we made about consumer preferences is violated in this case?Suppose 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 preferences. 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.
- Mrs. Rochester earns $4500 a week and spends her entire income on computers andpastries, since these are the only two items that provide her utility. Furthermore, a) Draw an indifference curve showing the optimum choice. Label the optimum aspoint A. What would be the marginal rate of substitution at the point thatcorresponds to the optimal consumption choice? Interpret the marginal rate ofsubstitution. b) What would be the new marginal rate of substitution that corresponds to theoptimal consumption choice? Interpret the marginal rate of substitution. c) Assume for this question only that when the price of computers decreases, less ofthat good is demanded. Illustrate the income and substitution effect of this pricedecrease.A consumer has the following utility function: U(x, y) = y + x1/2. Let px and py bt the corresponding prices and m her income. a). Write down the corresponding Lagrangian function and find the first order conditions (FOCs). b). Use these FOCs to find the expression for the marginal rate of substitution (MRS). Bearing in mind that the MRS is the slope of the indifference curve, what can you tell about the indifference curves of a quasilinear utility function?Suppose the two goods, are perfect complements at the ratio of 1 to 1. P1=10 and P2=40. I=1000. Find the optimal basket for this consumer, and graph it (including the budget line and the relevant indifference curve)
