13 Consider the following production function: Y = KALA Show that it represents constant returns to scale. Derive the demand for inputs, K, L, given their prices r and w, respectively. Calculate the long run cost functions for the firm for w-40 and r-10. What would be mininum cost for producing 200 units. What about 400? Is this firm experience economies of scale? Suppose that firm experienced financial constraint and will be allowed to use only 200 units of capital. Calculate the short run cost functions for the firm. What would be the cost of producing 200 and 400? Are the costs of producing 200 and 400 same in the short run and long-run? Draw the cost curves of the firm for the short run and long run.