The Production Function for the Begay & Lewis Company - Assignment Example

Ans 1.a ) The production function for the Begay & Lewis Company is Q = L0.3K0.3E0.1M0.18 Marginal products of input of L,M,K and E are given by MPL = dQ/dL = 0.3 L-0.7 K0.3E0.1M0.18 MPk = dQ/dk = 0.3 K-0.7 L0.3 E0.1M0.18 MPE = dQ/dE = 0.1 E-0.9 L0.3K0.3 M0.18 MPM = dQ/dM= 0.18 M-0.82 L0.3K0.3E0.1 (Webster, 5 -7) 1.b) The average average product of capital and labor is given by Average product of Labor = APL = Q/L = L0.3K0.3E0.1M0.18/ L = L-0.7K0.3E0.1M0.18 Average product of Capital = APK = Q/K = L0.3K0.3E0.1M0.18/ K = L0.3K-0.7E0.1M0.18 (Webster, 5 -7) 1.c) The marginal rate of technical substitution MRTS is given by MRTSKL = MPL / MPk MRTSLK = MPK / MPL K= $60,000,000 L = 4,000 MPL = 0.3 L-0.7 K0.3E0.1M0.18 = 0.3 (4000) -0.7 K0.3E0.1M0.18 = 0.3 (60,000,000)0.3E0.1M0.18 / (4000) 0.7 MPk = 0.3 (60,000,000)-0.7 L0.3 E0.1M0.18 =0.3 (4000)0.3 E0.1M0.18/(60,000,000)0.7 MRTSKL = MPL /MPk = (15000)0.7 (15000)0.3 = 15000 (Webster, 11, 214-15; Maddala and Miller, 174) 1.d) P = $2.00 (given) Pk = 1.8 (given) The firm should hire capital till the point the marginal value of capital equals its price. The return on capital is the marginal product of capital is and let is be denoted by ‘r’ P*r = Pk (value of input) Therefore, r = 1.8/2 = 0.9 per unit capital Cost of capital after the loan = 7.5 percent of $1.8 = .075*1.8 = $.135 pr unit capital. (Webster, 305) So this opportunity cost can be covered by the return (.9) which is higher than the former. Ans 2.a) TC = 1000 + 10Q2 MC = 20Q P= MC under competitive market P = 20Q Profit π = TR – TC = PQ – TC = 20 Q2 – 1000 - 10 Q2 π = 10 Q2 -1000 For profit maximization d π/Dq = 20Q (Webster, 267, 270) 2.b) TC = 1000 + 10Q2 MC = 20Q Now MC= P under competitive market. i) When P is given as 400 So MC = P = 400 Or 20Q = 400 Q= 20 Putting the value of Q in the profit function: Π = TR – TC = PQ – TC = 400(20) – 1000 - 10Q2 = 8000 – 1000 – 10 (400) = 3000 ii) When P is given as 2000 So MC = P = 2000 Or 20Q = 2000 Q= 100 Putting the value of Q in the profit function: Π = TR – TC = PQ – TC = 400(100) – 1000 - 10Q2 = 40000 – 1000 – 10(10000) = 39000 – 100000 = -61000 iii) When P is given as So MC = P = 3000 Or 20Q = 3000 Q= 150 Putting the value of Q in the profit function: Π = TR – TC = PQ – TC = 400(150) – 1000 - 10Q2 = 60000 – 1000 – 10 (22500) = 60000-1000- 225000 iv) When P is given as 4000 So MC = P = 4000 Or 20Q = 4000 Q= 200 Putting the value of Q in the profit function: Π = TR – TC = PQ – TC = 400(200) – 1000 - 10Q2 = 80000 – 1000 – 10 (40000) = 80000 – 1000 – 400000 = -61000 (Webster, 20-22) 2.c.) The fixed cost component of the above cost function TC = 1000 + 10Q2 Is 1000 (Webster, 20-22) 2.d) C = 32,000,000 -01.6Q1Q2 + 0.2Q12 + 0.66Q22. With respect to the above cost function we can say that we can have economies of scope as it is a multi product cost firm and It is cheaper to produce the two outputs jointly instead of separately. In the above example there is cost complementarity’s as a aQ1Q2 C(Q1 ,0) + C(0, Q2 ) = f + (Q1 )2 + f + (Q2)2 C(Q1, Q2) = f + aQ1Q2 + (Q1 )2 + (Q2 )2 f > aQ1Q2: Joint production is cheaper (Webster 29-33; Henderson and Quandt, 85- 178) Ans 3) Q = L0.3K0.3E0.1M0.18 we put in our multipliers and create our new production function. Increase all by ‘m’. Q’ = (K*m) 0.3(L*m) 0.3(E*m) 0.1(M*m)0.18 Q’ = K0.3L0.3 E 0.1 M0.18 m0.88 Q’= Q* m0.88 Since m > 1, then m0.88 < m. Our new production has increased by less than m, so we have decreasing returns to scale. (Maddala and Miller, 179) Ans 5 a.) Y = 4.8 + 8L + 4K, --------- (1) for L = labor and K = capital MPK= 4 MPL = 8 b) Y’ = 4.8 + 8(L*m) + 4(K*m) = 4.8 + m (8L + 4K) ------------(2) b) This follows increasing returns to scale, as Y’ is greater than Y. when m>1 We see that when Capital and labor are increased by a constant number then the output increases but at an increasing rate given m>1. (Maddala and Miller, 179) 5.c) The product Y will be produced under constant cost conditions when m=1. This will be possible when “factors of production are perfectly divisible and the production process does not permit division of labor. There should be no new specialized capital equipments. The level of production depends on firm’s choice with suitable application of capital, labor and raw materials. Under this condition, both small scale and large scale production would be equally efficient. Secondly, there should be a broad spread of output such that below that level scale economies can be met and above that scale diseconomies will result. So along this wide range of output the firm should be neutral about the scale economies. The cost of unit production along this range should be constant. In equation 2 above, if we put m=1, then Y’=Y (Mukherjee, Mukherjee and Ghose, 136). 6) a) Walker, Inc. has a legal obligation to purchase 2 tons of structural steel per week to manufacture conveyor frames. This is a contractual transaction. Sometimes pre informed agents can take advantage of agents who are relatively uninformed but who have unexpected needs to trade. Financial contracts endogenously provide a type of protection to the uninformed agents. These contracts have the distinctiveness of producing “security safe returns from underlying assets with certain returns” (Webster, 7). b) Exxon-Mobil makes use of the oil extracted from its wells to make raw polypropylene. This leads to a kind of vertical integration where a company increases its production into zones that are at diverse junctures of the production path. Vertical integration indicates amalgamation along a supply chain. For example, if a retailer begins to manufacture the products it markets, then it is growing its level of vertical integration. It is thus losing specialization and increasing its organizational costs. Here Exxon-Mobil is using its own extracted oil to produce plastic. It is a kind of expansion into related territories (Managerial Economics and business strategy, 7). c) Boat Lifts R Us buys common AC motors from a local distributor. This is a spot transaction over a period of time. It does not qualify as a contractual exchange or an example of vertical integration. By this they, evade costs of contracting and that of vertical integration (Managerial Economics and business strategy, 7). d) Hart Construction – a homebuilding contractor—purchases 50 pounds of nails from the local Burton Lumber company - This is a spot transaction where transactions can also be done for delivery on the same day or next day depending on the customer’s needs and depending on the market situation one can avoid costs of vertical integration. (Managerial Economics and business strategy, 7) Ans 7) SDL of the Innovation Campus of Utah State University develops optical tools for the Air Force Research Center at Kirkland Air Force Base in Albuquerque, New Mexico. Millions of dollars have been spent up front in R&D to set up the manufacture of these tools. These tools are used in defense experiments performed by the Air Force. This is a specialized investment where only two parties are involved and they both understand and have use for the product. Beyond the two parties the exchange relationship has no value or the products are unrecognized. In this case SDL takes up a specialized investment to manufacture optical tools for the Air Force. Beyond these two parties, there is no value use of these optical tools. This leads to higher transaction costs and hold up problems. Also here the type of specialization is dedicated assets. (Managerial Economics and business strategy, 7) Ans 8.a) PACAR and Massey Ferguson purchase their diesel engines for, respectively, heavy duty trucks, and tractors and harvesting equipment from, respectively, Cummins Engines Inc. and Perkins Diesel Inc. and have been making these purchase for some time. This is a case of contractual purchase. As the transactions have been going on for sometime and regularity is maintained. In presence of pre informed agents contractual transactions is used to hold onto safe returns and dedicated assets (Managerial Economics and business strategy, 5-7). b) PACAR and Massey Ferguson would like to purchase engines instead of manufacturing them, as manufacturing would involve specialized investments and vertical integration. It will increase the organizational costs; also parts of the business sheltered from competition can become less efficient as they are no longer subject to the discipline of competition. Contractual transaction would prevent specialized investment (Managerial Economics and business strategy, 5-7). Ans 9) Automobile manufacturers mainly produce their own engines but purchase mirrors from independent suppliers. This is because automobiles require specialized parts and engines and machinery which can be specifically produced by their own factories. The automobile companies set up huge factories, a type of specialized investment, to meet the demands and compete. Specializing gives them the ability to secure supplies and future orders and prevent hold ups. Mirrors are not a essential component. Neither does it fall under specialized investments. So the companies can acquire them from other companies which manufacture them. The automobile companies need not make huge investments to set up a glass factory. Buying mirrors from independent suppliers helps to sustain the competition amongst them, quality is ensured and also reduces input costs (Managerial Economics and business strategy, 5-7). Ans. 10) i) The marginal cost of writing a contract of length L is MC = 10 + 2L Marginal benefit = 100 At the optimal point the MC = MB, so the optimal length of the contract can be found out by placing 10 +2L = 100 2L = 90 L= 45. (Managerial Economics and business strategy, 10) ii) The marginal cost of writing a contract of length is MC = 10 + 2L When MB is 150, then at the optimal point MB = MC 10 + 2L = 150 or 2L = 140 L = 70 (Managerial Economics and business strategy, 10) iii) The marginal benefit usually rises in case of higher need of specialized investment. When the marginal benefit increases, then the marginal benefit curve, which is a flat curve, moves upward. When it moves upward, the optimal point is reached at a higher marginal cost. From the above sum we see that when the marginal benefit increased the optimal length of the contract became longer. In case the marginal benefit curve falls due lesser marginal benefits, then the intersection of the MC curve and MB curve occurs at a lower point and at a lesser marginal cost. The length of the contract is also lesser. In the above sum we saw that when the MB was 100, the length of the contract was 45 and when the MB was 150, the length of the contract was 70 (Managerial Economics and business strategy, 8). Ans 11.c) You hire an employee to operate a machine that only your company uses. This type of specialization involves human capital. The employees taken in to operate those machines would be the only ones to operate those. The machines are specific to that company, so the work force operating it is also acquainted to working on those. The company has to train them to work on those machines. This is thus an investment on human capital. Also it would be an example of physical asset specificity as only a certain type of machines is used (Managerial Economics and business strategy, 7). 11.d) An aerosol canning company designs a filling line that can be used only for a particular firm’s product. This is a specialization where the canning company has dedicated itself to its assets, or the firm from which it gathers the product. The canning company cannot use any other type of product as it would increase production costs significantly. This product specificity can of course lead to problems of price rise, or hold ups. The solution to that would be vertical integration. (Jones, Hill & Charles 316) 11.e) A food processor builds a frozen packaging/storage facility across the street from its primary buyer, All-America Food Service, a wholesaler to restaurants and fast food establishments. This is a kind of specialization where the food processor company is highly dependent on the primary buyer. It is not that its products are not bought by others; it is just that All- America Food Service is the primary buyer. This kind of specificity can be put under site specificity. This will reduce search costs, negotiation costs and other required investments or expenditures for the food processor plant (Managerial Economics and business strategy, 6, 7). Ans 12.) Pitney Bowes Office Services, Inc. – the fax and copier division of Pitney Bowes, Inc. signed a 5 year, $25 million contract for IT services from CGI Group, a Canadian information technology company. Contract is an extended relationship between two companies. By entering into a contract both ensure service and monetary exchange for a period of time. By locking themselves into a long- term contract with Pitney Bowes, CGI reduces the size of a potential entrant’s market, thereby reducing the probability of entry. As a result, other entrants will have to accept a higher price. For Pitney and Bowes a spot market sale is not really available. For CGI, it will have to take the services of Pitney and Bowes to service the printers and fax machines for a period of time. This servicing would be best done by the company providing the services and at a pre determined cost. The cost to CGI would then be less. It would prevent any specialized investment on the part of CGI. Most importantly the risk of opportunism can be prevented. It is also a case where both have equitable gain. Contractual safeguards also come in where services from Pitney Bowes can be considered only for CGI specifically and not to other companies. From the point of view of Pitney and Bowes a contract is a security with safe returns (Strategic Management: An Integrated Approach, 296) Ans.13.a) A&A Manufacturers needs to buy components for its manufacture of cell phones. A&A can get the components from Watts Telecommunications in Chicago, Wang Electronics in Taiwan, or Ghertsholz, A.G. in Frankfurt, Germany. A&A needs to know if the components meet cell phone transmission and radiation standards in the United Kingdom where the bulk of the cell phone sales are occurring. So they go to Taiwan and spend $2 million on testing to see if Wang’s components meet the standard. Then they get bids from Wang and the other two component vendors. The bids for the components come in at $100 million, $101 million and $103 million from, respectively, Watts, Ghertsholz and Wang. A company selects its alliance only after comprehensive research. The company collects information. Here A &A does the same. In trying to lower its input costs, it tries to test Wang technologies in Taiwan and if their products match the required standards. Opportunism refers to self interest with astuteness and incorporates the confiscation of markets or technology. Different events are occuring here. A&A moves out to Taiwan to test Wang Technologies and by doing so it is protecting its technology, design and development from competitors. Long term contracts are a way of preventing opportunistic behavior. The A&A company tests Wang Electronics so as to see if it adheres to its specifications and requirements. Long term contracts allow concerned parties to respond to opportunistic actions and thus controls opportunism. b) A&A can go forward with the contract with Wang Electronics. The contract prevents any withdrawal of a party suddenly. Also it insulates the parties from external changes that influence bargaining positions (Strategic Management: An Integrated Approach, 296). A&A should go for the contract with the Chicago based company as it had put forward the lowest bid (Strategic Management: An Integrated Approach, 296-298). References Henderson, James. M., Quandt,Richard E. Microeconomic theory: a mathematical approach ,Edition3, PublisherMcGraw-Hill, 1980 Maddala, GS., Miller, Ellen., Microeconomics: Theory and Applications, Tata McGraw-Hill, 2004 Managerial Economics and business strategy, Tata McGraw-Hill/Irwin. http://www.tau.ac.il/~gandal/lecture5.pdf Mukherjee, S. Mukherjee, M. & A. Ghose. Microeconomics, PHI Learning Pvt. Ltd., 2004 Webster, Thomas.J. Managerial economics: theory and practice, Emerald Group Publishing, 2003 Jones, Gareth R. and Hill, Charles W, Strategic Management: An Integrated Approach, Edition8, Cengage Learning, 2007 Read More