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Suppose ke is 5, there is no crowding out, and full-employment output is $600. Equilibrium output is initially $500 in Figure 8-1 for aggregate demand and aggregate supply curves AD1 and AS1. The recessionary gap is $100 since full-employment output is $600; the price level is initially p0. Since the expenditure multiplier is 5, a $20 increase in government spending should increase output $100 and bring output to its full-employment level when the price level remains at p0. This $100 increase in spending is presented in Figure 8-1 by the shift of aggregate demand from AD1 to AD2. Since aggregate supply AS1 is positively sloped, the price level rises from p0 to p1. This increase in the price level decreases private-sector spending; equilibrium output thus increases to $580 rather than to $600. Suppose the aggregate supply curve is AS2 rather than AS1. Figure 8-1 shows that the increase in aggregate demand from AD1 to AD2 raises the price level to p2 rather than p1, and equilibrium output is $540.

The Comparable interface requires the compareTo() method, as specified at line 2. The purpose of the method is to indicate whether the implicit argument is less than, equal to, or greater than the explicit argument. The indicator is the sign of the returned integer: Negative indicates that this < object, zero indicates that this = object, and positive indicates that this > object. In the case of ratios a/b and c/d, we can tell whether a/b < c/d by cross-multiplying and checking whether ad < bc. Since that case should be indicated by returning a negative number, we can simply return ad bc. Indeed, the value of that expression will be negative, zero, or positive, when a/b < c/d, a/b = c/d, or a/b > c/d, respectively. However, that arithmetic trick works only if b > 0 and d > 0. To ensure that the denominators are not negative, we employ the static utility method defined at line 14. It ensures that the denominator of its argument is not negative.

Figure 1.7 illustrates how the implementation of an interface is represented in UML. The association symbol is a dashed arrow pointing to the interface. The diagram for the interface marks its name with the stereotype interface . Note that an interface rectangle has only two parts, while a class rectangle has three. This is because interfaces have no fields. Figure 1.7 also illustrates how to represent package membership. The Comparable interface is part of the java.lang package, as indicated by the tab above the interface symbol. POLYMORPHISM

Java is a strongly typed language, which means that every variable must be declared to have a type which determines how that variable can be used. A char cannot be used where a boolean is expected, and a Ratio object cannot be used where a Person object is expected. But there are some situations where a variable of one type can be used where another type is expected. This is called polymorphism (literally, many forms ) because the object appears to have more than one type. There are several kinds of polymorphism. The simplest kind is called inclusion polymorphism. Illustrated in Example 1.8, it refers to the ability of an object to invoke a method that it inherits. EXAMPLE 1.8 Inclusion Polymorphism

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public class TestRatio { public static void main(String[] args) { Ratio x = new Ratio(22, 7); System.out.println("x.hashCode(): " + x.hashCode()); } }

Figure 8-1

The output is:

x.hashCode(): 1671711

At line 4, the Ratio object x invokes the hashCode() method that it inherits from the Object class.

CHAP. 1]

Note that there is a smaller increase in equilibrium output but a larger increase in the price level because aggregate supply curve AS2 is more steeply sloped than AS1.

Another kind of polymorphism occurs with generic methods, where an actual type is substituted in for a type parameter. This is illustrated in Example 1.9. EXAMPLE 1.9 Parametric Polymorphism

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Width in Pixels (WIDTH) Height in Pixels (HEIGHT) Visibility (VISIBILITY) With Tray (WITH_TRAY)

public class TestSort { public static void main(String[] args) { String[] countries = {"CN", "IN", "US", "ID", "BR"}; print(countries); Arrays.sort(countries); print(countries); Ratio[] ratios = new Ratio[3]; ratios[0] = new Ratio(22, 7); ratios[1] = new Ratio(25, 8); ratios[2] = new Ratio(28, 9); print(ratios); Arrays.sort(ratios); print(ratios); } static <T> void print(T[] a) { // generic method for (T t : a) { System.out.printf("%s ", t); } System.out.println(); } }

Here is the output:

CN IN US ID BR BR CN ID IN US 22/7 25/8 28/9 28/9 25/8 22/7 The print() method defined at line 16 is a generic method. It uses the type parameter T as a place-