Final answer:
The production function illustrates output based on input levels, with variable inputs such as labor differing from fixed inputs like equipment. An isoquant is derived by setting production to a constant, and the MRTS is calculated using marginal physical products of the variables. Calculating elasticity of substitution generally requires more data.
Step-by-step explanation:
To understand the concept of a production function, we should first differentiate between the different types of inputs or factors in a production function, which include fixed inputs and variable inputs. Fixed inputs cannot be easily changed in the short-term, whereas variable inputs can be adjusted depending on the level of production.
Using the given production function Y = x1² + 10x2 - x2², we can derive an isoquant by setting Y to a constant level of output and then solving for one variable in terms of the other. To find the marginal rate of technical substitution (MRTS), we take the partial derivatives (marginal physical products) of Y with respect to x1 and x2, which are MPP1 = 2x1 and MPP2 = 10 - 2x2 respectively. The MRTS is then MPP1 / MPP2. Assuming that x1 = 5 and x2 = 2, we substitute these values into the marginal physical products to calculate MRTS.
The elasticity of substitution between two inputs measures how easily one input can be substituted for another. It is calculated based on changes in the proportion of the input quantities and the MRTS. However, with the given information and function, calculating the exact elasticity would require more complex analysis that is not provided in the information given.
Improvements in technology often raise the capacity to produce more output with the same set of inputs, shifting the production function upwards. In the context of farms, a farmer could use better technology to increase the yield of crops without adding more labor or land.