As in the lemons model, suppose that there is one seller and one buyer who may exchange a good of quality v~ U[0, 1]. The seller, who values the good at v dollars, knows the value of v. The buyer, who values the good at 3v/2 dollars, does not know the value of v (only that it is uniformly distributed on [0, 1]). There is a fixed price of p = 1/2 at which trade may occur, which happens if and only if both the buyer and the seller agree to trade. Before deciding whether to trade, the buyer can pay a cost c € (0, 1) to learn the value of v. The seller's payoff is p if trade occurs and v if trade does not occur. The buyer's payoff is 3v/2-p-c if trade occurs and he first learned the value of v; 3v/2 - p if trade occurs and he did not learn the value of v; -c if trade does not occur and he first learned the value of v; and 0 if trade does not occur and he did not learn the value of v. Find the probability that trade occurs for each c € (0, 1).

Maintenance on an old machine is $100 this year but is expected to increase by $25 each year thereafter. What is the present worth of five years of the costs of maintenance? Use an interest rate of 10%.

could you explain step 2 more thoroughly please