Below is a production function for a firm that turns two variable factors of production, capital k and labor l, into a single output y. Labor is freely variable in the short and long run. Capital is fixed in the short run, but can be varied in the long run. Assume that the firm is a price taker in the factor markets, that the price of capital is r, and the price of labor is w. For each of the production function, what is the firm's long-run total (variable) cost function? In the short and in the long run, does the firm exhibit increasing, decreasing, or constant returns to scale?
f(k,l) = ak + (1 - a)l