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How to draw isoquant curves for a certain quantity? What does "increasing return to scale" and "decreasing returns to scale" mean? What is "capital input" if all I have is quantity of labor and total quqntity of product?

Typically, a production isoquant is drawn on a graph with labor on one axis, capital on the other. Because of decreasing returns to scale, isoquants have a concave shape (bow pointing towards the (0,0) point). The isoquant represents the mix of capital and labor that will produce a given, fixed level of output. (So, increasing labor and holding capital constant would move you to a higher isoquant. Substituting labor for capital could move you along the isoquant curve).

Increasing returns to scale: increasing an input by x% creates MORE than an x% increase in output. For example, two construction workers, working together, can build more than twice as fast as one worker working alone).
Decreasing returns to scale: increasing an input by x% creates LESS than an x% increase in output.

Im not sure how to answer your last question. If your only input is labor, then your optimal isoquant will be a "corner" solution -- where the isoquant crosses the labor axis. Ergo, capital input is zero.

Or do you have a problem where you know the amount of labor and you know total output and you are asked to determine the efficient amount of capital used?

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