Final answer:
The question examines the relationship between the cost function, input demand functions, production function, and returns to scale in the context of a firm's operations. Exponents a and b in the cost function relate to input costs, while d determines returns to scale. The production function and conditional input demand functions can be inferred from the given cost function.
Step-by-step explanation:
The question involves understanding how the cost function is related to the firm's production function and how inputs are used to produce outputs.
Specifically, the firm's cost function, c(w1, w2, q) = wa1 wb2 qd, is given, and we are asked to determine what can be inferred about the exponents a, b, and d.
(a) The exponents a and b represent the degree to which each input contributes to the total cost and are related to the elasticity of substitution between the inputs.
The exponent d relates to the output quantity and its relationship with the costs, impacting the returns to scale.
(b) To find the conditional input demand functions, we would normally derive the cost function with respect to w1 and w2, while holding output constant.
The production function would be inferred by considering that the cost function is derived from it, essentially requiring us to work backward from the cost function to determine the production function.
(c) The returns to scale can be identified by analyzing the exponent d. If d is greater than 1,
the firm experiences increasing returns to scale; if d is less than 1, it experiences decreasing returns to scale; and if d equals 1, it experiences constant returns to scale.