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[MZ, BR, PT, MO, GW, CV, AO] it1.next(): MZ it1.next(): BR it1.next(): PT it1.next(): MO [MZ, BR, PT, GW, CV, AO] it1.next(): GW [MZ, BR, PT, CV, AO] MZ BR PT CV AO it1.next(): CV The Iterator object it1 is instantiated at line 6 and returned by the iterator() method. Bound to the port collection, it visits the elements in the same order as they were printed at line 5. Note that this

6 gives the marginal revenue product. It is obtained from the increase in the total revenue in column 5. b. The MPP that results from employing each additional unit of the variable resource (together with xed amounts of other resources) declines because of the law of diminishing returns. The MRP declines because MPP declines. We know that this rm is a perfect competitor in the product market because product price remains constant at $1 per unit regardless of the quantity of the product sold by the rm. Solved Problem 16.3 Explain how much of each variable resource a rm should hire in order to maximize total pro ts, if the rm is an imperfect competitor in the resource markets. Solution: When an imperfect competitor in the resource markets wants to hire more of a resource, it will have to pay a higher price, not only on the additional units of the resource but also on all previous units of the resource hired. Thus, the increase in the total costs of hiring an additional unit of the resource or marginal resource cost (MRC) exceeds the resource price. The rm will maximize total pro ts when it hires variable resources as long as each resource MRP exceeds its MRC and until they are equal. With variable resources labor (L) and capital (K), the rm maximizes total pro ts when MRPL = MRCL and MRPK = MRCK. Another way of stating the pro t-maximizing condition is to say that a rm should hire resources until the MRP per dollar spent on each resource is the same. Once again, this rule can be extended to any number of variable resources.

order is not the same as the order in which the elements were added to the collection. Since the collection is a set, its elements have no intrinsic order. It is the iterator itself that computes the traversal sequence. You can see from the output from line 5 that the toString() method (invoked implicitly by the println() method) uses the same traversal sequence, obviously using its own iterator to build the string. The it1 iterator s remove() method is invoked at lines 11 and 14. This causes it to delete the current element, which in each case is the last element returned by a call to next(). At line 11, the last next() call was at line 10, which returned the MO element; so MO is deleted by remove() at line 11. Similarly, at line 14, the last next() call was at line 13, which returned the GW element; so GW is deleted by remove() at line 14. These deletions are evident from the output produced by the while loop at lines 17 19. Notice that that loop uses the independent iterator it2 to traverse the collection. Note that the code at lines 16 19 make a complete traversal of the collection. This is guaranteed by the instantiation of the new iterator at line 16 and the use of the hasNext() method to control the loop. The last output, generated at line 21, confirms that the two iterators it1 and it2 are independent. The action of it2 had no effect on it1, which returns the CV element at line 21.

CHAP. 4]

out first. That means that each element is assigned a priority number, and the element with the highest priority comes out first. Priority queues are widely used in computer systems. For example, if a printer is shared by several computers on a local area network, the print jobs that are queued to it would normally be held temporarily in a priority queue wherein smaller jobs are given higher priority over larger jobs. Priority queues are usually implemented as heaps since the heap data structure always keeps the element with the largest key at the root and its insertion and removal operations are so efficient. According to Theorem 13.1, those operations are guaranteed to run in in O(lgn) time. THE JCF PriorityQueue CLASS The Java Collections Framework includes a PriorityQueue class. As Figure 4.1 on page 70 shows, that class extends the AbstractQueue and AbstractList classes, implementing the Queue and List interfaces. EXAMPLE 13.6 The java.util.PriorityQueue Class

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