For the next three problems, let's now consider a firm that faces discrete demand from two types (Y&Z) of customers. The following table describes the customers' maximum willingness to pay for the firm's product: First Unit Second Unit Type Y $20 Type Z $25 $6 $12 Let's suppose there are 100 of each type of customer and the firm has a constant marginal cost of $5. #4.) If the firm is aware of the above table and can identify the type of each and every customer, then how much profit can the firm make by engaging in first-degree price discrimination? What is the consumer surplus and total social surplus under first-degree price discrimination? #5.) Suppose the firm cannot identify the type of individual customers but is aware of the above distribution. Let's consider a pricing strategy where the firm can charge $P per unit, but gives a discount of D% on the second unit (buy one and get the second one at D% off). (a) What is the optimal price P and second unit percentage discount D? (b) Find the firm profit, consumer surplus, and total social surplus associated with this 2nd degree price discrimination strategy. #6.) Suppose the firm must engage in a single uniform price per unit (no price discrimination). What would that optimal price be? Find the firm profit, consumer surplus, and total social surplus associated with this uniform price.