Suppose an economy with a continuum of individuals with unit mass. There are n types of individuals, where a type i person produces good i, but consumes good i + 1, except type n produces good n and consumes good 1. There are 1/n individuals of each type, and each individual is randomly matched with one other individual each period. Let x = 1/n . Assume that in every meeting of two individuals, neither individual knows anything about the other individual’s past – there is assumed to be no memory. Goods are produced and consumed in one-unit quantities, where c is the cost of production, and u is the utility for an individual from consuming the individual’s preferred good. Individuals discount the future at rate r. In the first period, M individuals are each endowed with one unit of indivisible money. Each individual can hold either one unit or zero units of money, and cannot produce if they are holding money. Suppose, at the beginning of each period, the government chooses a individuals at random who are currently holding money, takes their money, and gives it to individuals who do not have money. This government intervention occurs before meetings occur during the period between individuals. Assume that 0 < a < M. (a) In an equilibrium in which money is traded, determine the effects of a change in a on the value of holding money, and the value of holding no asset. (b) Determine the conditions under which the equilibrium in part (a) exists, and determine how a affects those conditions. Also, determine whether the government intervention, that is a > 0, affects economic welfare, relative to the case where it doesn’t intervene (a = 0). Explain what is going on.
Suppose an economy with a continuum of individuals with unit mass. There are n types of individuals, where a type i person produces good i, but consumes good i + 1, except type n produces good n and consumes good 1. There are 1/n individuals of each type, and each individual is randomly matched with one other individual each period. Let x = 1/n . Assume that in every meeting of two individuals, neither individual knows anything about the other individual’s past – there is assumed to be no memory. Goods are produced and consumed in one-unit quantities, where c is the cost of production, and u is the utility for an individual from consuming the individual’s preferred good. Individuals discount the future at rate r. In the first period, M individuals are each endowed with one unit of indivisible money. Each individual can hold either one unit or zero units of money, and cannot produce if they are holding money. Suppose, at the beginning of each period, the government chooses a individuals at random who are currently holding money, takes their money, and gives it to individuals who do not have money. This government intervention occurs before meetings occur during the period between individuals. Assume that 0 < a < M.
(a) In an equilibrium in which money is traded, determine the effects of a change in a on the value of holding money, and the value of holding no asset.
(b) Determine the conditions under which the equilibrium in part (a) exists, and determine how a affects those conditions. Also, determine whether the government intervention, that is a > 0, affects economic welfare, relative to the case where it doesn’t intervene (a = 0). Explain what is going on.
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