Two big questions, one applied, one theoretical.

1) Cobb-Douglas Functions. They confuse me. So if a production function is x^.3y^.7, we know that the demand for x will be .3m/px, demand for y will be .7m/py? Do they exponents HAVE to add up to 1?

2) Homework problem: "The two graphs on the back show two indifference curves for a Cobb-Douglas utility function. Consider a consumer who has income m = 20 and faces prices p1 = 1, p2 = 1. Suppose the price of x1 increases to 4. Use the first graph to show the Compensating variation, second graph to show Equivalent.

I get the 'pivot/shift' concept. But don't we need the Cobb-Douglas function to derive the demand functions to find these variations?

I realize that intial: x + y = 20, and I can draw that line.

Final: 4x + y = 20, can draw that line.

But how do I find the shift necessary in income if I don't know the equation. When I draw the line on the graph it runs tangent to the indifference curve at approx. point (10, 10) for initial. Can I use this? For the final budget line, it would be tangent at about (2.5, 10), which makes mathematical sense.

Thanks!