Array.prototype.reduce() is good for stuff like this: to perform aggregate operations (like min, max, avg, etc.) on an array, and return a single result:

myArray.reduce(function(prev, curr) {
    return prev.Cost < curr.Cost ? prev : curr;
});

...or you can define that inner function with ES6 function syntax:

myArray.reduce((prev, curr) => prev.Cost < curr.Cost ? prev : curr);

If you want to be cute you can attach this to the Array prototype:

Array.prototype.hasMin = function(attrib) {
    return (this.length && this.reduce(function(prev, curr){ 
        return prev[attrib] < curr[attrib] ? prev : curr; 
    })) || null;
 }

Now you can just say:

myArray.hasMin('ID')  // result:  {"ID": 1, "Cost": 200}
myArray.hasMin('Cost')    // result: {"ID": 3, "Cost": 50}
myEmptyArray.hasMin('ID')   // result: null

Please note that if you intend to use this, it doesn't have full checks for every situation. If you pass in an array of primitive types, it will fail. If you check for a property that doesn't exist, or if not all the objects contain that property, you will get the last element. This version is a little more bulky, but has those checks:

Array.prototype.hasMin = function(attrib) {
    const checker = (o, i) => typeof(o) === 'object' && o[i]
    return (this.length && this.reduce(function(prev, curr){
        const prevOk = checker(prev, attrib);
        const currOk = checker(curr, attrib);
        if (!prevOk && !currOk) return {};
        if (!prevOk) return curr;
        if (!currOk) return prev;
        return prev[attrib] < curr[attrib] ? prev : curr; 
    })) || null;
 }

You can use lodash's methods

_.max([4, 2, 8, 6]);
returns => 8

https://lodash.com/docs/4.17.15#max

_.min([4, 2, 8, 6]);
returns => 2

https://lodash.com/docs/4.17.15#min