Homework #6 ECN 100 Dear ECN 100, Using the quite reasonable assumption that the major goal of the firm is to operate in a way to maximize profits,...

(1)Marginal revenue is the addition to a firm’s total revenue when the firm produces one additional unit of output and sells this unit of output at the market price. Knowing that MR = dTR/dq, prove that the marginal revenue to the firm is usually below but at under specific conditions equal to the average revenue (AR) of the firm.(2)Given your answer in (1) above, what must we know about the price elasticity of demand on the demand curve when a firm lowers in price in order for total revenue (TR) to rise, pretty much stay the same, or fall?(3)What is meant my atomaticity in a market? In a market where atomaticity exists, what does this means for the price elasticity of demand facing a firm. What is the shape of thedemand curve facing this firm? What does this mean for the relationship between MR, AR, and P at the profit maximizing point of production for the firm?(4)Your firm faces a short run average cost curve SRAS that has an average cost per unit of output at $6.00 at its minimum point. Your firm faces a demand curve that falls below the minimum point of the SRAS. What should the firm do in the short run? If the firm follows your advice in the short run, what is the firm maximizing or minimizing? If the demand curve remains where it is, what should the firm do in the long run? In the REAL WORLD, if in the long run, the firm wants to be successful, what two main choices does it have?(5)Why is the marginal cost curve the supply curve for a firm that maximizes it profits? Explain your answer with a graph. Show the areas of profits for any price that the firm may face.(6)Let’s pretend that you are in the shelter-building business. You construct dwellings for people in your community.However, you are losing money in your business. You are in the short run. You are able to determine your cost schedule (SRAC and SRMC curves) as well as the demand function that you face. Draw your current situation on a graph.You decide that you want to stay in the shelter business as you wait for the long run. What must happen on your graph to make this possible and how do you intend do go about changing the conditions shown by your graph.(7)Now, from (6) above, assume that in the shelter-building business, you use capital and labor (your time, effort, mind-power, etc.) to produce your shelters. Your cost curves from (6) employ a cost-minimizing strategy. You build five shelters a month. Draw an isoquant diagram that illustrates where you are in the SR money-losing situation. So, according to your diagram, you could do better cost-wise and still be able to build the five monthly shelters. What condition(s) have to be met for you to be sure that you are truly minimizing your costs of production at the rate of 5 shelters per month?As you move into the long-run (LR), assume that you are indeed successful in remaining in business. How might you show the achievement of this success on your isoquant diagram?(8)When the demand curve facing a firm shows a willingness to pay that is always less that the average cost of output, what should the firm do in the SR? If this situation does not change in the LR, what should the firm do?(9)If a firm strives to maximize profits, is a price taker in both the product and factor markets, and is hiring labor and capital as factors of production, what rule must it follow with respect to the cost and productivity of the two factors AT THE MARGIN?How would you show this as a proof? HINT: Begin with – profits – TR – TC.(10)As a shelter-builder, you want to make more money in order to buy more stuff for your leisure time (digital cameras, iPhone 5, designer jeans, etc.). So, you lower your price of individual shelters from $1000 to $950. At this point in time, the price elasticity of demand that you face is (-) 1.04. Was this a good move for you? Now, what if you had been selling 30 shelters per month at the old price and now 31 shelters per month at the new price? What does this say about the price elasticity of demand and whether or not your price drop strategy was correct?(11)You face a demand curve that is – q = 20 – p.Calculate the marginal revenue curve.Assume that you face a constant returns to scale production function and your MC = $5.00.Draw a graph showing the demand curve the MR curve and the cost curves. (AC and MC).Now, you are able to produce an output, “x” that maximizes your profits. Calculate your profits.(12)In (11) you reduce your constant returns to scale costs by $1.00. You cut your AC by $1.00. What are profits when maximized?