Using IQ map and Iso-cost line, explain the concept of least cost combination of two inputs under given total cost outlay. What will be the effect on…

The least-cost combination is the input mix at which a producer, spending a given total cost outlay at given input prices, reaches the highest attainable output — found where the iso-cost line is tangent to the highest reachable iso-quant.

The least-cost combination under a given outlay:

1. Iso-quant map: a set of iso-quants, each showing combinations of labour and capital that yield a given output, with higher curves representing higher output.
2. Iso-cost line: the line C = wL + rK showing all input combinations the producer can buy with the given outlay C, where w is the wage and r the price of capital.
3. Slope of the iso-cost line: it equals the input-price ratio w/r.
4. Slope of the iso-quant: it equals the marginal rate of technical substitution, MRTS = MPL/MPK.
5. Producer's goal: with a fixed outlay, the rational producer wants to reach the highest possible iso-quant.
6. Equilibrium (necessary condition): this occurs where the iso-cost line is tangent to the highest attainable iso-quant, so MRTS = MPL/MPK = w/r.
7. Sufficient condition: the iso-quant must be convex to the origin at the tangency point.
8. Interpretation of tangency: at point E the rate at which the producer can technically substitute the inputs equals the rate at which the market lets them trade the inputs, so no cheaper mix can produce that output.
9. Non-optimal points: combinations inside the iso-cost line are affordable but produce less (wasteful), while those outside are unaffordable.
10. Meaning of least cost: the tangency simultaneously gives maximum output for the outlay and minimum cost for that output — the least-cost combination.

The effect of a change in the total cost outlay:

11. Parallel shift: since input prices are unchanged, a rise in the outlay shifts the iso-cost line outward parallel to itself, and a fall shifts it inward parallel.
12. New tangency: each new iso-cost line is tangent to a new, higher (or lower) iso-quant, giving a fresh least-cost combination.
13. Output effect: a larger outlay lets the producer reach a higher iso-quant, so output rises; a smaller outlay pushes them to a lower iso-quant, so output falls.
14. Expansion path: joining these successive tangency points traces the expansion (scale) path, showing how the least-cost input mix changes as the firm scales output up or down.
15. Nepal example: a furniture maker whose budget rises can move to a higher iso-quant and build more tables, with the tangency point shifting along his expansion path.

The least-cost combination is the tangency of the iso-cost line and the highest attainable iso-quant (MRTS = w/r), and when the outlay changes the tangency shifts along the expansion path — output rising with a bigger outlay and falling with a smaller one.