(Solved): The one-input production function for a firm is given by q=2L, where q denotes output and L deno ...

The one-input production function for a firm is given by $$q=2\sqrt{L}$$, where $$q$$ denotes output and $$L$$ denotes hours of labor input. The firm is a price-taker both for output (which sells for $$p$$ ) and for workers (which can be hired at a wage rate of $$w$$ per hour). Describe intuitively why these functions have the form they do: - $$TC(w,q)$$ (decreases/increases) with $$w$$ and $$q$$. - $$?(p,w)$$ (decrease/increase) with $$p$$ and (decrease/increase) with $$w$$. - $$q(p,w)$$ (decreases/increases) with $$p$$ and (decreases/increases) with $$w$$. - $$L(p,w)$$ (decreases/increases) with $$p$$ and (decreases/increases) with $$w$$. - Also profit function (supply function, input demand function) is homogeneous of degree $$(0/1)$$ in (input and/or output) price(s)