Derive isocost line when total cost outlay is Rs.4000, wage rate is Rs.200 and rental rate of capital is Rs.400.

The isocost line represents all combinations of labor (L) and capital (K) that can be purchased with a fixed total cost outlay (C). Given:

• Total cost outlay (C) = Rs. 4000
• Wage rate (W) = Rs. 200
• Rental rate of capital (R) = Rs. 400

The isocost line equation is derived as follows: $$C=W\cdot L+R\cdot K$$ $$4000=200L+400K$$

Rearranging to express labor (L) in terms of capital (K): $$200L=4000-400K$$ $$L=\frac{4000-400K}{200}$$ $$L=20-2K$$

Thus, the isocost line equation is: $$L=20-2K$$

Final isocost line equation: $$\boxed{L=20-2K}$$