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HW9_SOLN - The figure above illustrates the supply and...

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Let D denote the number of people buying tickets. Let Pr[W] denote the probability of winning the prize. Then D is a function of Pr[W] and we denote that as D (Pr[W]). Pr[W], in turn, is a function of D denoted by Pr[W]( D ). Demand: The number of people that will buy a ticket will increase as the probability of winning increases. So, our demand function D (Pr[W]) is an increasing function. To simplify, let s assume it is linear. Supply: Take, as an example, the case where only one person buys a ticket. Assuming there is only one prize, then the probability of winning Pr[W](1) = 100%. Likewise Pr[W](2) = 50%, Pr[W](3) = 33.33%, and so on. Then, our supply function, Pr[W]( D ), is a decreasing function in D , with the rate of decrease diminishing as D gets larger. Let s graph our supply demand curves:
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Unformatted text preview: The figure above illustrates the supply and demand curves for the given situation. The curves intersect at point ( Eq ), which represents the equilibrium point of the system. If Pr[W] < Pr[W] Eq (below Eq in the figure), then we may have a situation where we are producing too many tickets (surplus) as the winning probability is too low to sell all the tickets. On the other hand, if Pr[W] > Pr[W] Eq (above Eq in the figure), we are producing too few tickets (shortage) and as there is an incentive for more people to purchase tickets, we could be making better profit. At Eq , there is no shortage or surplus; so Eq is a desirable point for both demand and supply sides. Eq Pr[W] Eq D Eq Demand Curve D Pr[W] Supply Curve...
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HW9_SOLN - The figure above illustrates the supply and...

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