Productivity is the rate of production of biomass expressed in terms of
(i) `("kcal"m^(-3))yr^(-1)`
(ii) `g^(-2)yr^(-1)`
(iii) `g^(-1)yr^(-1)` (iv) `("kcal"m^(-2))yr^(-1)`

Options

A. (ii)
B. (iii)
C. (ii) and (iv)
D. (i) and (iii)

Answer

To determine the correct units for measuring productivity, we need to understand the definition of productivity in the context of biomass production.

### Step-by-Step Solution:

1. **Understanding Productivity**:
- Productivity refers to the rate of production of biomass in an ecosystem. It is typically measured in terms of energy produced (like kilocalories) or biomass produced (like grams).

2. **Identifying the Units**:
- The units provided in the question are:
- (i) `("kcal"m^(-3))yr^(-1)`
- (ii) `g^(-2)yr^(-1)`
- (iii) `g^(-1)yr^(-1)`
- (iv) `("kcal"m^(-2))yr^(-1)`

3. **Analyzing Each Option**:
- **Option (i)**: `("kcal"m^(-3))yr^(-1)` - This unit suggests energy per cubic meter per year, which is not commonly used for productivity as it does not relate to surface area or biomass directly.
- **Option (ii)**: `g^(-2)yr^(-1)` - This unit suggests grams per square meter per year, but the negative exponent is incorrect for biomass measurement.
- **Option (iii)**: `g^(-1)yr^(-1)` - This unit suggests grams per year, but it lacks the area component necessary for productivity measurement.
- **Option (iv)**: `("kcal"m^(-2))yr^(-1)` - This unit suggests energy per square meter per year, which is a valid measurement for productivity.

4. **Conclusion**:
- The correct units for measuring productivity in terms of biomass are:
- **(ii)** `g m^(-2) yr^(-1)` (grams per square meter per year)
- **(iv)** `("kcal"m^(-2))yr^(-1)` (kilocalories per square meter per year)

### Final Answer:
The correct options for measuring productivity are **(ii)** and **(iv)**.