Explain the producer's equilibrium with two variable inputs using isoquants and isocost lines, and explain the expansion path and ridge lines.

1. 1 · Introduce the long run. All inputs are variable; the firm chooses its mix of labour and capital.
2. 2 · Define isoquant and MRTS. Properties: downward, convex, non-intersecting, higher = more output; MRTS = MPL/MPK, diminishing.
3. 3 · Define the isocost line. wL + rK = C; slope −w/r. Example: Rs. 100,000 buys 50 workers or 20 machines, slope −0.4.
4. 4 · Draw the equilibrium. [Diagram: isoquant map, isocost line tangent to one isoquant at E; L on the horizontal axis, K on the vertical]
5. 5 · State the conditions. MRTS = w/r, i.e. MPL/w = MPK/r; isoquant convex. Show the check with MPL = 40, MPK = 120.
6. 6 · Expansion path and ridge lines.
   • Expansion path joins tangencies as the budget grows
   • Upper ridge line: MPK = 0
   • Lower ridge line: MPL = 0
   • Economic region lies between them
7. 7 · Sri Lankan business link. Apparel firms move towards automation as wages rise relative to machine costs.
8. 8 · Conclude. The least-cost input mix is set by technology (isoquants) and input prices (isocosts).

Scoring tip: Draw ridge lines as two rays from the origin on the isoquant map and shade the economic region between them.