12 May DOES SOMEBODY NEED TO SMACK SOME SENSE INTO THEM?5.7 [5 POINTS] IS IT BETTER TO BE A RUDE NOMOPHOBE?
Econ 308Prof. ArtunçSpring 2016Problem Set 3: Technology AdoptionDue: April 20, 2016This problem set will be easiest if done with a spreadsheet, but that is up to you. Be careful to labelall results and discuss them as much as is needed for clarity.This problem set has 5 questions. Make sure you do them all. You should round your answers belowto three decimal places.Two countries, called Westeros and Braavos, are the subject of considerable economic competition.Westeros industrialized first but Braavos is fast catching up. Observers in Westeros are worried aboutthis development and are proposing lots of reasons why Westeros is losing first place. The point ofthis problem set is to help you evaluate one set of explanations.The following things can be taken as given for both countries:(i) All firms are owned by profit-maximizing entrepreneurs.(ii) All inputs are supplied on competitive markets. All firms are price takers in these markets.(iii) All outputs are sold on competitive markets. All firms are price takers on these markets, as well.All firms produce according to a Cobb-Douglas production function. This production function shouldlook familiar to you. It says that output Q is related to inputs K and L as:Q = AK?L”.This production function implies that the cost-minimizing demand for capital will be:K =??w”r?” ?QA?(1)where w is the wage rate, r is the cost of capital, Q is output level, and ? and ” are parameters. Wewill assume that ? + ” = 1; this is the constant returns to scale assumption we saw earlier in thecourse. âAâ is a technical parameter; an increase in âAâ means that the same amount of inputs yieldsmore output. You should be able to see that A is another name for the total factor productivity figurein an earlier problem set.Similarly,L =? “r?w?? ?QA?. (2)(Note that this function already imbeds the optimal combinations of capital and labor; this assumesthat the firm is producing as cheaply as possible, given its technology and factor costs. If you takemath econ you will learn how to derive all of this. For now you can take these are formula into whichyou plug numbers).1Question 1 [15 points]The cost of producing one unit of output can be written C = rK +wL, where K and L are the optimalinputs of capital and labor from the equations above. Using your high-school algebra, plug K and Linto the equation C = rK + wL, and show that the share of cost that goes to capital (rK/C) is equalto ? and the share of cost that goes to labor (= wL/C) is equal to “. Show us your steps! [Hint: startwith noting that rK/C = rK/(rK + wL)]Note that by assumption, an increase in ? implies a reduction in “. For given values of r and w, ahigher ? necessarily means that the firm uses relatively more capital in its production process. Makesure you understand this point.Question 2 [8 points]Assume that in both Westeros and Braavos, the following data hold: ? = 0.2, ” = 0.8, w = 1, r = 3,A = 2.2.1 [4 Points] How much does it cost to produce 1 unit of output in Westeros? 1 unit of output inBraavos?2.2 [4 Points] Suppose now that the following table characterizes the production functions in the twocountries (they are still both Cobb-Douglas, but they have different parameter values):? in Westeros 0.2″ in Westeros 0.8? in Braavos 0.4″ in Braavos 0.6A = 2 in both countries.If factor costs are still the same in the two countries, how would you expect product techniques todiffer? Which country would use relatively more capital to produce a unit of output? (Do you need tocalculate the actual amounts of capital and labor used, or can you make an argument just based onthe information provided, without any more calculations?)Question 3 [8 points]3.1 [4 points] A variety of observers admire firms in Braavos for using new, capital-intensive methods.These methods are only rarely used in Westeros. Using the following table and the formulas providedabove, tell us whether this difference reflects a more âmodern spiritâ among factory owners in Braavos.You can assume that A=2 in both countries, still, if you need that number to answer the question.Explain the economic intuition behind your answer.Westeros Braavos? 0.3 0.3″ 0.7 0.7w 1 1r 3 13.2 [4 Points] Westeros industrialists are always saying that they would look more like Braavos if theyreceived a tax write-off for additional capital investment. What do you think of that claim?2Question 4 [34 points]The world is always much messier than in economics problem sets. Westeros and Braavos are competingfiercely in the world market for soap. There are two technologies for making soap, the Old and theNew. Here are some important facts.Braavos invented the new technology, so it can use that New technology without paying anyroyalties.There are two firms in Westeros, Lannister and Stark. Lannister was founded by a personwho co-discovered the New technology. It can also use the New technology without paying anyroyalties.Stark is allowed to use the New technology, but for every unit it produces this way it has to pay$1 to the Braavos firm and to Lannister (50 cents to each, that is, for a total payment of $1 perunit produced).The Old technology has ? = 0.3, ” = 0.7. The New technology has ? = 0.7, ” = 0.3. With the Oldtechnology A = 2, and with the New, A = 5.The following table gives input costs. Note that both Westeros firms face the same input costs sincethey are in the same factor markets.Westeros Braavosw 1 3r 4 44.1 [8 Points] Assume that demand is such that each Westeros firm can expect to sell 3 units, no moreand no less. Which technology should Lannister use? Which should Stark use? Remember to bear inmind the royalty costs!4.2 [6 Points] A string of critics have savagely attacked Westeros industry, claiming that it is slow toadopt new production methods. Their favorite example is the fact that some Westeros firms use oldtechnologies long after their Braavos competitors have switched to something else. Considering ourexample only (your answer in 4.1, that is). Do you think this is a fair criticism? If Westeros is at fault,how is it at fault? If you had complete control over Westeros, what would you propose as a way tomodernize Westeros industry (again, drawing only on the example given in 4.1).4.3 [12 Points] There is a big feud among the owners of the New technology. They withdraw all licensesand begin shopping their patent around. They make the following offer to all Westeros firms and toall Braavos firms: without our patent you have to use the Old technology again. But for a per-unitpayment of Z we will let you use our New technology.Ignore all costs of re-equipping factories, etc. What is the maximum Z for a Westeros firm? For aBraavos firm? Why are these numbers different? What if anything does this say about the quality ofbusiness leadership in the two countries?If you were the ruler of Westeros, what would you do to encourage the use of New technology? Wouldthis make any sense as a policy goal?4.4 [8 Points] The King of Westeros has a keen interest in all this business. He makes the followingargument to a meeting of Westeros soap makers: The production function for New has a larger valueof A. This âAâ shows that the same amount of inputs and outputs produces more soap with New thanwith Old. Thus all soap makers everywhere should use New. The King does not criticize his own soapmakers, so you need not revisit the questions asked in 4.2 and 4.3 But the King notes that none of thesoap makers in the former colony of Pentos use New. When the owners of the New technology triedto sell soap makers in Pentos the right to use New, none were interested, not at any price. The Kingsays this reflects the inherent stupidity of Pentosian soap makers.A Pentosian who hears the Kingâs remarks points out that in Pentos capital is scarce and costs $8 perunit, while labor is cheap and costs $1 per unit. Thus, the man says, only a fool would use New inPentos. The Kingâs police seize this Pentosian and force him to listen to 30 hours of post-modernistranting. At the end of his sentence he speaks constant gibberish and, in fact, sounds like an ASUstudent. The harshness of the punishment aside, do you think the King was right, or was this poorPentosian?Question 5 [35 Points]For the following question, you can assume firms value each year at the same rate (in other words,they do not discount the future). You can also assume that each year, the demand is fixed and doesnot change. You can make other (more involved) assumptions, but this is the simplest.Slurms are invented in year zero and can only be produced for 5 years. In year 6 anyone caughtproducing these rare extracts of Wormulan excrement will be forced to translate the works of theEnglish department into English. Two technologies are invented; the Old is the first technology, andat the end of year 2 someone invents a New technology.Suppose that the unit cost of making Slurms with the Old technology looks like this:C = !A + 4wwhere A is a technology parameter and w is the prevailing local wage. To use this technology theentrepreneur pays $750 in a fully sunk cost (that is, if she shuts down she gets nothing back, and theplant has no scrap value). The plant lasts 5 years and then disappears. It is equally productive in allof those 5 years and requires no maintenance whatsoever.Suppose now that the New technology for producing slurms comes along in year 2 (at the end; so thereare 3 years left). The technology here is:C = !B + 3w.Once again, the investment in this new technology lasts 3 years, is equally productive in each of thoseyears, and requires no maintenance. This technology also requires a $750 irrecoverable cost.Many entrepreneurs invest in the Old technology at the outset. Some entrepreneurs had to waitbecause they were too busy playing with their smart phones in class and were forced to write âI am arude nomophobeâ on the board 10,000 times. But when finished they still want to produce them tastyslurms.5.1 [5 points] Do the nomophobes use the Old or the New technology?5.2 [5 points] Do any of the original investors (using Old) switch from Old to New when New comesalong?5.3 [5 points] Does anyone switch later on?5.4 [5 points] How, if at all, does each of these decisions depend on the size of the market?Wherever possible solve for the decision rule that determines their action and explain the economicrationale behind it. What elements drive each decision? Make sure to tell us what happens, and onwhat it depends (both the stuff we list here, and other things).5.5 [5 points] What does this have to do with Britain and Germany at the end of the 19th century?5.6 [5 points] If you observed somebody who is not a nomophobe producing with the Old technologyin year 5, what would you conclude? Does somebody need to smack some sense into them?5.7 [5 points] Is it better to be a rude nomophobe?5
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Order Now” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.