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- Which 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 correctwhat is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPiiGiven 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.
- 16. Utility functions are simply mathematical representations of preferences.(a) True(b) FalseUtility 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?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?
- Existence of representative consumer Suppose households 1 and 2 have one-period utility functions u(c1) and w(c2), respectively, where u and w are both increasing, strictly concave, twice-differentiable functions of a scalar consumption rate. Consider the Pareto problem: Subject to the constraint c1 + c2 = c. Show that the solution of this problem has the form of a concave utility function vθ(c), which depends on the Pareto weight θ. Show that vθ(c) = θu (c1) = (1 − θ)w (c2). The function vθ(c) is the utility function of the representative consumer. Such a representative consumer always lurks within a complete markets competitive equilibrium even with heterogeneous preferences. At a competitive equilibrium, the marginal utilities of the representative agent and each and every agent are proportional.Suppose a consumer is indifferent between the bundles (x1, x2) = (19, 10) and (15, 16), and suppose that the same consumer prefers the bundle (15, 14) to both. What can you say about his/her preferences when evaluated against standard assumptions of consumer preferences?Which form of utility is expressed on ranking the bundles According to preferences
- Wherein:TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Expected Monetary ValueGive an example of monotonic preferenceShow the derivation of the individual demand function for a utility maximizer consumer and explain the common properties for the points on the fuction which you show.