Assume a market with many individuals who trade goods. The number of goods available for trade grows as time evolves. In the first period, there is only one good to trade, in the second period, two goods, and so on (obviously in the Nth period there are N goods). Suppose that the market arrangement (and preferences of individuals) is such that the probability an individual engages in trading is inversely proportional to the number of goods: if there is only one good, the probability of trading is 1; if there are N goods, the probability of trading is 1/N. The payoff if an individual trades is 1 and if she does not, the payoff is zero. Suppose that individuals can create a monetary system every period for which they all have to pay a cost equal to 0 < x < 1. This system, however, raises the probability of trading for all individuals to 1 irrespective of the number of goods available in the market. After how many periods will individuals in this market decide to pay for this monetary system? Note that individuals decide whether to pay for the monetary system before they look for trades. (Hint: what is the expected payoff for a given individual if there is no money? How about if there is money? At which point are these equal?).