Edit in JSFiddle

var Core = {
    screenwidth: "1024px",
    init: function () {
        this.render();
    },
    render: function () {
        $('#container').css("width", this.screenwidth).html("Default Render Function");
    },
    utli: function () {
        $('#container').append("<p>Core utility function Called</p>");
    },
};

var desktopLib = {
    init: function () {
        this.screenwidth = "600px";
        this.render();
        this.utli();
    },
    render: function () {
        $('#container').css("width", this.screenwidth).html("Desktop Render");
    }
};

$(document).ready(function () {
    desktopJS = $.extend(true, Core, desktopLib);
    desktopJS.init();
});

<div id="container"></div>