Suppose you are working for a firm producing a new, innovative product. You are the only producer of this good. The cost function is given by ??(??) = 500 1 2 ??2, and you have paid a market research firm to assess the demand for your good. They estimate that the market demand curve is ??= 1,000 2??. a) Is this the short run or long run? b) If the firm is currently charging a price of $325, are they making a profit? c) Should the firm change the price they are charging? What price should they charge? Show your work! d) Given your recommendation to (b) and (c) above, by how much would the firm's profits increase