Production Theory

A production function displays increasing returns to scale when the sum of the exponents of the inputs is greater than 1. This means that when all inputs are increased by a constant factor, the output increases by a larger factor. Given that Q(x, y) = Ax^ay^b, and we know a + b = 2, which is greater than 1, this indicates increasing returns to scale.

In other words, doubling the inputs will lead to more than double the output. Thus, the correct answer is (c) Increasing returns to scale.

Since the odd numbers are twice as likely as the even numbers, the total probabilities must add up to 1. By assigning proper weights to each outcome, we can calculate the probability of getting a result greater than 3 (i.e., 4, 5, or 6).
The correct answer is 95​.
Hence, the correct answer is (d).

Step 1: Understanding the production function.
A production function that is homogeneous of degree one satisfies Euler's equation: where is the output, is capital, and is labor. If , this suggests diminishing returns to labor.

Step 2: Analysis of options.
- (A) will be negative: This is incorrect. Marginal product of labor cannot be negative if the production function is still in the positive range.
- (B) will be zero: This is incorrect. is greater than , so it cannot be zero.
- (C) will be negative: This is incorrect. We don't have enough information about capital to assert that is negative.
- (D) and will both be negative: This is correct because when marginal products are decreasing, both labor and capital may experience negative marginal returns at certain levels of output.

Step 3: Conclusion.
The correct answer is (D). When marginal product of labor exceeds the average product, both and may be negative.

Step 1: Reasons for holding inventories.
Firms hold inventories for reasons such as meeting future demand, smoothing production, or dealing with uncertainties in supply.

Step 2: Analysis of options.
- (A) To meet future demand for goods: This is correct. Firms hold inventories to ensure they can meet customer demand even when production is not immediate.
- (B) It is more costly for a firm to order goods less frequently in large quantities than to order small quantities frequently: This is incorrect. Generally, ordering goods in large quantities less frequently is more cost-effective due to economies of scale.
- (C) To smoothen the production process: This is correct. Inventories help to ensure a smooth production process by ensuring that raw materials and components are available when needed.
- (D) Some inventories are held as an unavoidable part of the production process: This is correct. Certain inventories are needed for production, such as work-in-progress inventory.

Step 3: Conclusion.
The incorrect statement is (B), as ordering in bulk is typically cheaper than ordering in smaller quantities frequently.

Step 1: Understanding the production functions and their forms.
- **Translog Production Function (A):** This function allows for flexibility in functional forms. Its functional form is ** **. This corresponds to **(I)** in List-II.
- **Generalised Leontief Production Function (B):** This production function is characterized by a linear combination of input quantities raised to a power. Its form is ** , where **. This corresponds to **(II)** in List-II.
- **Cobb Douglas Production Function (C):** This is a widely used production function in economics. Its functional form is ** , where **. This corresponds to **(III)** in List-II.
- **Constant Elasticity of Substitution Production Function (D):** This function expresses the relationship between inputs and outputs in terms of elasticity. Its form is ** **. This corresponds to **(IV)** in List-II.

Step 2: Conclusion.
The correct answer is **(A) - (I), (B) - (II), (C) - (III), (D) - (IV)**.