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Solved Problem 14.1 a. Draw a gure showing, for a monopolist, the best level of output. Include three alternative AC curves, showing that the rm (1) makes a pro t, (2) breaks even, and (3) incurs a loss. b. What would happen to this monopolist in the long run if it incurs short-run losses Short-run pro ts Solution: a. In Figure 14-2, the best level of output for the monopolist is OB, given by point C where MR = MC. With AC1, the monopolist makes a per-unit pro t of GF and a total pro t of GF times OB. With AC2, P = AC and the monopolist breaks even. With AC3, the monopolist incurs a perunit loss of HG and a total loss of HG times OB. Only if P > AVC (so that TR > TVC) will the monopolist stay in business and minimize short-run total losses by producing OB. b. If the monopolist has short-run losses, it could, in the long run, build a more appropriate scale of plant to produce the best long-run level of output. The monopolist might also advertise in an attempt to cause an upward shift in the demand curve it faces. (This, however, will also shift cost curves up.) If this monopolist still incurs a loss after having considered all of these possibilities, it will stop producing the commodity in the long run. If the monopolist was already making short-run pro ts, it will still build the most appropriate plant in the long run and increase total pro ts.

public class TestSieve { private static final int SIZE=1000; private static BitSet isPrime = new BitSet(SIZE); public static void main(String[] args) { initializeSieve(); ch02.pr20.TestSieve.printSieve(); } private static void initializeSieve() { for (int i = 2; i < SIZE; i++) { isPrime.set(i); } for (int n = 2; 2*n < SIZE; n++) { if (isPrime.get(n)) { for (int m = n; m*n <SIZE; m++) { isPrime.clear(m*n); } } } } private static void printSieve() int n=0; for (int i = 0; i < SIZE; i++) if (isPrime.get(i)) { System.out.printf("%5d%s", } } System.out.printf("%n%d primes } } { { i, ++n%16==0 "\n":"");

less than %d%n", n, SIZE);

TRAN Example of documents for InfoProvider data: Comments on various characteristic values ( Sales for material 4711 in Germany were poor in May because ... or In May the following key figures were interesting: Delivery quantity Explanation ..., Outstanding payments .... )

public class Primes { private static final int SIZE = 1000; private static int size = SIZE; private static BitSet sieve = new BitSet(size); private static int last = 1;

CHAP. 2]

static { for (int i=2; i<SIZE; i++) { sieve.set(i); } for (int n=2; 2*n<SIZE; n++) { if (sieve.get(n)) { for (int m=n; m*n<SIZE; m++) { sieve.clear(m*n); } } } } public static void setLast(int n) { last = n; } public static void setLast() { last = 1; } public static void setSize(int n) { size = n; } public static void setSize() { size = 1000; } public static boolean isPrime(int n) { return sieve.get(n); } public static int next() { while (++last<size) { if (sieve.get(last)) { return last; } } return -1; } public static void printPrimes() { int n=0; for (int i=0; i<SIZE; i++) { if (sieve.get(i)) { System.out.print((n++%10==0 "\n":"\t")+i); } } System.out.println("\n" + n + " primes less than " + SIZE); } }

Figure 14-2

public static String factor(int n) { public static String factor(int n) { String primes=""; int p = next(); while (n > 1) { if (n%p==0) { primes += (primes.length()==0 "":"*") + p; n /= p; } else p = next(); if (p == -1) { primes += " OVERFLOW"; break; }

} setLast(); return primes; }

public class TestGoldbach { public static void main(String[] args) { Primes.setSize(1000); System.out.println("4 = 2+2"); for (int n = 6; n < 100; n += 2) { System.out.print(n); for (int p = 3; p <= n/2; p += 2) { if (Primes.isPrime(p) && Primes.isPrime(n-p)) { System.out.print(" = "+p+"+"+(n-p)); } } System.out.println(); } } } public class TestFermat { public static void main(String[] args) { Primes.setSize(1000); for (int p = 0; p < 5; p++) { int n = (int)Math.pow(2,Math.pow(2,p)) + 1; if (Primes.isPrime(n)) { System.out.println("p = "+p+", n = 2^2^p = "+n); } } } } public class TestBabbage { public static void main(String[] args) { Primes.setSize(1000); for (int x = 0; x < 50; x++) { System.out.print(x); int n = x*x + x + 41; if (Primes.isPrime(n)) { System.out.println("\t"+n+" is prime"); } else { System.out.println(); } } } } public class TestTwinPrimes { public static void main(String[] args) { Primes.setSize(1000); int n = Primes.next(); while (n < 0.9*N) { if (Primes.isPrime(n+2)) { System.out.println(n + "\t" + (n+2)); } n = primes.next(); } } }

CHAP. 2]