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Which of the following is the correct statement?
1. The slope of the Isoquants represents the MRTS
2. The MRTS of the inputs x and y = $$\frac{{{\text{M}}{{\text{P}}_{\text{x}}}}}{{{\text{M}}{{\text{P}}_{\text{y}}}}}$$
3. The elasticity of substitution between two inputs x and y is proportionate change in the ratio of two inputs divided by proportionate change in the MRTS
4. If degree of homogeneity is greater than one, the production function is increasing returns to fixed factor
On the expansion path of the firm operating with homogeneous production function, which among the following remain constant?
1. Input ratio
2. Price ratio of inputs
3. Marginal rate of technical substitution between the factors
4. Elasticity of substitution
Select the correct answer
Indicate the correct answer from the following types of the long run average cost curves on which the minimum average cost of production in long run can be determined.
1. Long run average cost curve under normal production function
2. Long run average cost curve under linearly homogeneous production function
3. Planning curve
4. Envelope curve
The elasticity of substitution between two inputs in CES production function
The short-run production function for a firm is as follows
Q = -L3 + 15L2 + 10L
Where Q denotes total output in physical units and L denotes units of labour which are homogeneous, but are not perfectly divisible and change in labour does not tend to become zero.
Statement I In this production function, the marginal product of 5th unit of labour is 85.
Statement II Similarly, in this production function, the average product of the 5th unit of labour is 60.
A significant property of the Cobb-Douglas production function is that the elasticity of substitution between inputs is
The given bar graph represents data of the production of paper (in ten lakh tonnes) by three different companies X, Y and Z during the years 2008 to 2012. The x-axis shows the 'years' and the y-axis represents the 'production of paper (ten lakh tonnes)'. (Note: The data shown is only for mathematical exercise. They do not represent actual figures.)  The total production of Company Y during 2008 and 2009 and Company X for 2011 and 2012 taken together is p% (p is correct to the nearest integer) more than the total production of Company Z during 2010, 2011 and 2012. The total production of Company Z during 2008 and 2009 taken together is q% (q is correct to the nearest integer) less than the total production of Company X during 2008, 2009 and 2012 and Company Y during 2010 and 2011 all together.  What is the positive difference between p and q ? 
Consider the following statements regarding homogeneous mixture. Identify the correct ones. A homogeneous mixture is a liquid, gaseous & solid mixture that has similar proportions throughout its components.  Salt and pepper form is a pure example of a homogeneous mixture.
What is the general form of the general solution of a non-homogeneous DE (uh(t)= general solution of the homogeneous equation, up(t)= any particular solution of the non-homogeneous equation)?
There are five crude oil refining companies in India namely, A, B, C, D, and E. Statements: I. The production of Company B is more than that of Company A but not more than that of Company E. II The production of Company C is more than the production of Company B but NOT as much as that of Company D. III. The production of E is NOT as much as the production of Company D. Which of these statements is/are sufficient to answer the question that the production of which of the following companies is the highest?