Why the following variables (x1, x2 and x3) cannot be the Marshallian demand functions of a consumer with well–behaved preferences, even when pa ≥ pc. x1(p,y)= y/2pa x2(p,y)= (pc y)/2pa pb x3(p,y)= (pa-pc)y/2pa pc HINT: Use properties of the Marshallian demand function to check this.
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Why the following variables (x1, x2 and x3) cannot be the Marshallian
functions of a consumer with well–behaved preferences, even when pa ≥ pc.
x1(p,y)= y/2pa
x2(p,y)= (pc y)/2pa pb
x3(p,y)= (pa-pc)y/2pa pc
HINT: Use properties of the Marshallian demand function to check this.
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- Under the ordinal theory, a consumer is expected to rank his or her scale of preference from the least to the most satisfying. From this knowledge, describe the assumptions of the ordinal utility theory With the help of illustrations, show how the consumer attains equilibrium under the indifference curve approach As a student of microeconomics, use the knowledge attained during the teaching-learning process and show how the demand curve is derived under the cardinal theory approach .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.Suppose the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where p1,p2 > 0. a) Plot the indifference curves b) Find the Marshallian demand functions. Show graphically the utility maximizing choices.
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- Consider the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)Consider an individual with the following utility function: Derive step-by-step both corresponding Hicksian demand functions depending on the different prices (P₁, P2) and a fixed utility level u. The equation given In picture.do This in 10 minutes.Is optimal consumption basket the same as associated level of utility?
- Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1, x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns? (A) preference for flflexibility; (B) context effffects; (C) time inconsistency; (D) intransitivity.The preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…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 correct
