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    Public Economics Assignment Vaishali V, HS10H039  1. Explain why the economy will be closer to an efficient equilibrium when congestion occurs with a small club membership level A club good is a good that is either nonrivalrous or partly rivalrous, but for which exclusion by the  providers is possible. This concept of exclusion implies that the act of voluntarily choosing to become a member of a club is a form of preference revelation, which has important implications for the attainment of market efficiency. While clubs and local public goods have been treated interchangeably, the discussion of the former has focused more on issues of efficiency with homogenous populations. The analysis of club goods includes not only the quantity of good or service to be provided, but also the size of the club membership so as to prevent congestion. In the simplest model of a club, that is, with a homogenous population of consumers who are identical in terms of taste and income and where one private and one club good is provided, the decision to be made relates to how much of the club good to supply and how many members to admit. Suppose each consumer has a utility function U(x,G,n)  where  x  is the consumption of a private good, G   provision of the club good and n  the number of club members. Then utility increases in  x and G , but decreases in n if there is congestion. If the cost of providing G units of the club good is C(G) , then the  budget constraint of a member with income  M   when the cost of the club is shared equally between members will be   The decision problem is then to choose G  and n  such that the welfare of a typical member is maximized. This can be expressed as  *+   The first-order conditions for this optimization problem produce the following equations:            (1)            (2)   Here equation (1) describes the Samuelson’s rule describing the level of public good G the club should supply and equation (2) describes the efficient level of membership for the club.    Two cases emerge in the analysis of economy wide efficiency of club goods. In the first case, the efficient size of the club is small relative to total population. This applies when the club suffers from significant congestion so that the size of the efficient club membership is small relative to the size of the total  population. The other situation is when the efficient size of the club is large relative to the total population due to limited congestion or a smaller population. The economy will be closer to an efficient equilibrium in case of small clubs due to the following reason. Suppose the population of the economy increases in size. Initially, with a small population, there will be (a) Some of the population who are not in the optimally sized club or else (b) Every club will different slightly in size from the optimum. In (a), as the size of the population increases, the number of those who are not in an optimally sized club  becomes trivial compared to the total population and the deviation from efficiency tends to zero. In (b), as  population increases, the deviation of each club from the optimum size becomes less and less and thus again the inefficiency tends to zero. In both cases, an increase in the population size eventually wipes out the deviations from efficiency. If the population size is infinite, then it can be divided exactly into an infinite number of optimal size clubs, where the provision of the public good is efficient for each club and the economy as a whole. Thus, if the efficient membership of each club is small relative to the total population, a large number of clubs will be formed with each having the correct number of members and providing the efficient level of services, leading to efficiency for the economy as a whole. 2. Using signaling model construct an example in which a government unaware of workers’ productivity can improve the welfare of everyone compared to the separating equilibrium by means of cross-subsidization policy but not by banning signaling In the presence of asymmetric information where either party has more information on the good being  purchased or sold than the other, mechanisms such as signaling and screening can help improve the market efficiency. Signaling for instance, is a mechanism by which the more informed players in the market signal to the less informed players about the quality of the product so that both parties can be  benefited by the process. Some examples of signaling include employment references in the labor market and warranties in the durable goods market. Signaling is different from screening as in the former, more-informed players use signals to help the less-informed players find out the truth about the product, unlike the latter where the less-informed players used mechanisms to get more information about the product.  For a signal to be effective, it must satisfy certain criteria. First, it must be verifiable by the receiver or the less-informed agent. Second, it must be credible and finally the signal must be costly for the sender to obtain and the cost must differ between various qualities of the sender. This also means the signaling model revolves around the timing of actions, where the informed agent moves first and invests in acquiring a costly signal. Equilibrium is reached when the chosen investment in the signal is optimal for each informed agent and the inferences of the uninformed about the meaning of signals are justified by the outcomes. A basic model of productivity signaling in the labor market is considered below. Suppose there are two identical firms which compete for workers through the wages they offer. The set of workers can be divided into two types depending on their productivity  –   low-productivity and high-productivity. It is also assumed that without any signaling, the firms cannot judge the productivity of the worker. In this case, the workers can signal their productivity by being educated. Education itself does not alter  productivity, but it is costly to acquire. Investment in education will thus be worthwhile if it can earn a higher wage. To make it an effective signal, we assume that obtaining education is more costly for the low-productivity worker than for the high-productivity one, so that both do not have the same incentives for acquiring it. Let     denote the productivity of a high-productivity worker and    denote the productivity of a low- productivity worker with     >   . The workers are present in the population in proportions  λ h and  λ l , such that  λ h +  λ l = 1. The average productivity in the population is given by            Competition between both firms ensures that this is the wage that would be paid if there were no signaling and the firms could not distinguish between workers. Further, for a worker of productivity level  , the cost of obtaining education level e is   which satisfies the property that any given level of education is more costly for a low-productivity worker to obtain. The firms offer wages that are potentially conditional of the level of education and the wage schedule is denoted by w(e) . Hence the decision problem of the workers is to maximize wages less the cost of education as shown below.

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