The correct answer is: A. a-1, b-2, c-3
A production function is a mathematical relationship that shows the maximum amount of output that can be produced from a given amount of inputs. The returns to scale of a production function are the relationship between the amount of inputs used and the amount of output produced when all inputs are increased by the same proportion.
Constant returns to scale occur when a production function exhibits a linear relationship between inputs and outputs. This means that if all inputs are increased by a factor of 2, then output will also increase by a factor of 2.
Diminishing returns to scale occur when a production function exhibits a decreasing relationship between inputs and outputs. This means that if all inputs are increased by a factor of 2, then output will increase by less than a factor of 2.
Increasing returns to scale occur when a production function exhibits an increasing relationship between inputs and outputs. This means that if all inputs are increased by a factor of 2, then output will increase by more than a factor of 2.
In the given question, the production function in option (a) is Q = 10.2K0.19 L0.88. This production function exhibits constant returns to scale because the exponents of K and L add up to 1.
The production function in option (b) is Q = 1.01L0.75 K0.25. This production function exhibits diminishing returns to scale because the exponent of K is less than 0.5.
The production function in option (c) is Q = 0.84L0.63 K0.3. This production function exhibits increasing returns to scale because the exponent of K is greater than 0.5.
Therefore, the correct answer is: A. a-1, b-2, c-3