Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions: V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py Where Mi is the income level of person i and Px and Py are the prices for goods x and goods y, respectively. a) Calculate the market clearing prices.
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Consider a two-person exchange economy in which initial endowments for both individuals are such that (e1 = e1) = (1,1). Suppose the two individuals have the following indirect utility functions:
V1 (x, y) = ln M1 - a ln Px - (1-a) ln Py
V2 (x, y) = ln M2 -b ln Px - (1-b) ln Py
Where Mi is the income level of person i and Px and Py are the
- a) Calculate the market clearing prices.
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- Please draw its diagram Consider the following pure exchange economy with two consumers and two goods. Consumer 1 has utility given by U1 = min {4x1, 2x2} Consumer 2 has utility given by U2 = 2x1 + x2 The initial endowment has consumer 1 starting with 200 units of x1 and 200 units of x2. Consumer 2 starts with 300 units of x1 and 300 units of x2. Draw an Edgeworth box diagram for this initial endowment complete with the indifference curves for each individual.A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. a) The surplus associated with cooperation is S = Z − Yh − Yw. Show that each spouse consumes his or her fallback income plus half the surplus in the Nash cooperative bargaining solution. Please do fast ASAP fast please.A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. What do Ch and Cw equal if Yh = Yw (but this quantity is not equal to zero)? Please do fast ASAP fast
- Bluth’s preferences for paper and houses can be expressed as Ub(p, h) = 2pb + hb, while Scott’s preferences can be expressed as Us(p, h) = ps + 2bs. Bluth begins with no paper and 10 houses, whereas Scott begins with 10 units of paper and no houses. 1. Is the starting endowment Pareto efficient? Justify your answer using an Edgeworth box? Determine whether each of the following price pairs is consistent with a competitive equilibrium. If yes, determine the resulting allocation of goods, sketching that equi- librium in your Edgeworth box. If not, explain why not (for what good is there a shortage, for what good is there a surplus?) pp =$3 and ph =$1 along with pp =$1 and ph =$1 Assume that the price of houses is $1. Given that price, determine the highest price pp that is consistent with a competitive equilibrium.In a standard economic model, we generally assume the individual only cares about their own payoff. So, for example, utility of individual i is given by u = pi, where pi is the individual’s payoff. Suppose the individual is playing a dictator game with another partner j. How would you modify the utility function to explain the non-zero allocations to the partner that are typically observed?Consider a pure exchange economy, where each consumer has preferences described by a Cobb-Douglas utility function. Both consumers have exactly the same endowment. In such an economy, an equitable distribution of goods (where each individual consumes exactly half of each good) is a Walrasian equilibrium allocation. a. always for any consumers' preferences b.only if consumers' preferences are exactly the same c. never d. non of the above
- There are two firms, whose production activity consumes some of the clean air that surrounds our planet. The total amount of clean air is K > 0, and any consumption of clean air comes out of this common resource. If firm i ∈ {1, 2} uses ki of clean air for its production, the remaining amount of clean air is K − k1 − k2. Each player derives utility from using ki for production and from the remainder of clean air. The payoff of firm i is given by ui(ki , kj ) = ln(ki) + ln(K − ki − kj ) j ≠ i ∈ {1, 2}. (a) Assuming that each firm chooses ki ∈ (0, K), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs?Modified True or False: State whether each statement is true or false. If the statement is false, briefly explain why it is so, and then restate it to make it true. k. Pareto efficiency or Pareto optimality is a condition where no change is possible that will make some members of society better off without making some other members of society worse off.Points on a utility possibility curve represent a given distribution of well-being between two persons an efficient allocation of resources the maximum well-being of any one person, given the resources available and the well-being of another person all of the above
- Q16 Pareto optimality refers to the maximum efficient allocation of economic resources such that there is no way that one's wealth another person worse off: this statement is choices - irrelevant -conditionally true -always true -always falseA typical consumer has a well-behaved preference structure for his consumption bundle which includes only two goods, A and B. assume that commodity A is normal and commodity B is inferior. By keeping commodity A on the x-axis and commodity B on the y-axis you are required to show the price decomposition for commodity B when $PB increases exogenously relative to $PA. Please Answer the question by using well labelled diagrams. Show that Cobb-Douglas preferences are homothetic preferences