Deep Copy of Object

/* Write a JavaScript function clone(obj) that accepts as parameter an object of reference type.
The function should return a deep copy of the object. Write a second function compareObjects(obj,
objCopy) that compare the two objects by reference (==) and print on the console the output given below. */

"use strict";

function clone(obj) {
    var deepCopyObj = new obj.constructor();
    for (var property in obj) {
        if (obj.hasOwnProperty(property)) {
            switch (typeof obj[property]) {
                case 'object':
                    deepCopyObj[property] = clone(obj[property]);
                    break;
                default:
                    deepCopyObj[property] = obj[property];
                    break;
            }
        }
    }

    return deepCopyObj;
}

function compareObjects(obj, objCopy) {
    return 'a == b --> ' + (obj == objCopy);
}

var a = {name: 'Pesho', age: 21};
var b = clone(a);
console.log(compareObjects(a, b));

var a = {name: 'Pesho', age: 21};
var b = a;
console.log(compareObjects(a, b));

var a = {name: 'Joro', age: 24, exams: { 'C#': 6, 'Java': 5, 'WebFunds': 6, 'JavaScript': 6, 'Python': 4}};
var b = clone(a);
console.log(compareObjects(a, b));