Give correct solutions.
It is estimated that 16% of the cost of goods sold represents fixed factory overhead costs and that 22% of the operating expenses are fixed. Since Royal Cola is only one of many products, the fixed costs will not be materially affected if the product is discontinued. a. Prepare a differential analysis, dated March 3, to determine whether Royal Cola should be continued (Alternative 1) or discontinued (Alternative 2). If an amount is zero, enter zero "0". Use a minus sign to indicate a loss. Differential Analysis Continue Royal Cola (Alt. 1) or Discontinue Royal Cola (Alt. 2) January 21 Differential Effect Continue Royal Discontinue Royal on Income Cola (Alternative 1) Cola (Alternative 2) (Alternative 2) Revenues Costs: Variable cost of goods sold Variable operating expenses Fixed costs Income (Loss) Should Star Cola be retained? Explain. As indicated by the differential analysis in part (A), the income would by if the product is discontinued.II. Now, suppose both countries can trade with each other and Honda enters the US. market while Ford starts selling in Japan. Suppose global demand is then doubled to Q=Q1+Q2=2'(1002pla where Q1 is Ford's quantity and Q2 that of Honda. Assume that the marginal cost of both companies is equal to M C = 20. 1. 2. Solve the demand for the price P as function of the quantities Q1 and Q2. Ford's prots are [[1 = P - Q1 M C - Q1. Plug in your result from (1) for P and write down the rm's rst-order condition with respect to Ford's quantity Q1. . Whenever 2 rms are symmetric and have the same marginal cost like in this case, they will choose the same quantities and so Q1 = Q2. Use this and the result from (2) to show that Ford and Honda are optimally going to produce a quantity of 40 each. . Show that the new equilibrium price is 30. Is it higher or lower than the price you found in the monopoly case? Briey explain why. . Compute Ford's prots when its fixed cost are still F = 400. What does this tell you about the impact of entry on prots? Suppose that Honda's xed cost is slightly higher and equals 500. Would Honda stay in the market or will Ford be a monopolist in this case as in part I? . A common xed cost for rms is related to product standards: When selling in Eu rope for example, many US. rms need to adjust their products to meet European regulations and laws. Recent negotiations on trade agreements therefore often call for more harmonization of product standards to reduce this type of cost. Suppose that this would reduce Honda's xed cost to 400. Based on your results for the previous parts, would this benet consumers? Why or why not? 2. Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400 - P, so the inverse demand is P = 400 - Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model we imagine that the two firms simultane- ously choose their production or quantity, and that demand (market clearing) determines the price given each firms' quantity. (a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts like a monopolist and sets output where MR = MC)? Hint: The first firm's inverse demand is P = 400 - (Q1 + Q2), but since Q2 = 0 we can write this as P = 400 - Q1 and so MR = 400 - 2Q1 Mathematically this problem is the same as a monopoly problem. What quantity will firm 1 choose? What price will it charge? What is the producer surplus and profit? (b) Now suppose instead that the second firm produces exactly 100 units, and that the first firm anticipates this. The total output is the first firm's output, Q1, plus 100, so substituting Q1 + 100 for Qrot in the inverse demand implies that P = 300 - Q1. That is, if firm 1 produces Q1 it expects the price to be 300 - Q1. This implies that firm 1's revenue is 300Q1 -Q; and firm 1's marginal revenue is MR = 300-201. How much will firm 1 produce (set MR = MC)? What price will clear the market given the total output Q1+ @2? What is the producer surplus and profit? (c) Explain intuitively why neither firm wants to change their production if each is producing 100 (Q1 = Q2 = 100)? Note that your are explaining why Q1 = Q2 = 100 is a Cournot-Nash equilibrium). (d) Calculate the total producer surplus (both firms) and consumer surplus in part (a) and (b). Why is consumer surplus higher with 2 firms than with one firm? (e) Intuitively, why is the dead weight loss smaller with two firms than with only one firm?2) What is the equation for marginal revenue when this monopolist sells to both classes, but cannot distinguish between the two classes? Add the MR curve to your graph. (Hint: you should have two equations to express the MR curve for the monopolist.) 3) Complete the following: The quantity the monopolist produces: Qu = The monopolistic price: PM = The quantity demanded by Class I: Q, = The quantity demanded by Class II: Q. = Consumer surplus for Class I: CS I = Consumer surplus for Class II: CS II = The monopolist's profit: a = 4) Draw two graphs: on the first graph represent Class I demand and on the second graph represent Class II demand. Shade the area that represents CS I on the first graph and the area that represents CS II on the second graph: label these areas clearly. c) Now suppose that the monopolist can identify buyers from each class. Also assume that buyers from one class cannot resell the good to buyers from the other class. The monopolist will practice third-degree price discrimination by setting separate prices, P, and P, for Class I and Class II respectively. 1) What is the marginal revenue equation for Class I (MR,)? Draw a graph which shows the demand and marginal revenue curves for Class I. Label these curves clearly. 2) What is the marginal revenue equation for Class II (MR.)? Draw a graph which shows the demand and marginal revenue curves for Class II. Label these curves clearly. 3) Complete the following: The quantity sold to Class I: Q, = The quantity sold to Class II: Q. = The price charged to Class I: P, = The price charged to Class II: P, = Consumer surplus for Class I: CS I = Consumer surplus for Class II: CS II = The monopolist's profit: a =Part 2 Consider the endogenous growth model in which time can be used for work (it) or human capital accumulation (1 15). Output is produced according to Y = zuH, where z is total factor productivity and H is the current stock of human capital. The future human capital stock is given by H ' = M] u)H, where 5 represents eiciency in producing new human capital. The initial (current) human capital stock is H = 100. The economy is characterized by the following parameters: b = 6.1, 2 = 15, and u = 0.83. (a) Calculate future human capital (H '), and the growth rate of human capital. (b) Calculate current output (Y), future output (1\"), and the growth rate of output. How does it compare to the growth rate of human capital? (c) Suppose the government cuts technology funding for education, and as a result b declines to b = 6.0. Calculate the growth rate of output following this change. ((1) Are the growth rates you found in parts a and c the same or different? Explain intuitively why this policy change did or did not a'ect the economy's growth rate. (e) Explain how the decrease in b will affect (if at all) the current levels of human capital, output, and consumption: H, Y, and C. If there is no effect, explain why. (f) Explain how the decrease in b will affect (if at all) the future levels of human capital, output, and consumption: H', Y' , and C' . If there is no effect, explain why. (g) Explain how the decrease in b will affect the growth rates of human capital, output, and consumption. If there is no effect, explain why. (h) Draw a graph of logoutput, ln'), over time for this economy and illustrate how the decrease in b affects current and future output. 1. (55 points) Consider the Solow growth model. Output is produced every period ac- cording to the following production function: Y = = F(K, N), where = is total factor productivity, and F() satisfies the usual assumptions. The capital stock accumulates according to K = (1 - 6)K + sY, where 0
