# ECO 304K HOMEWORK #5 INTRO MICRO Fall 2014

1. Consider the following two projectsProject A: Costs $12,000 today. Increases profit by $3000 next year, $7,200 intwo years, and $4000 in three years.Project B: Costs $7500 today. Increases profit in two years by $8190Both projects have no value beyond the given time frames. A firm faces a rate toborrow money of 9% and has the option of investing money with almost no risk at5%.a) If the firm has $25,000 on hand, with only these two project to choose from,will they invest in A, B, neither or both? Show the calculations that lead to yourconclusions. Explain whether you answers would be different for either project ifthe firm had no money on hand to invest. (1 point)b) Explain, based on your calculations in (a), why the rate of return on project Amust be somewhere between 5% and 9%. Set up (but do not solve) andequation that would find the rate of interest where the firm is indifferent betweeninvesting in project A, and not investing in project A. (1 point)d) Use the data in (a) to bound the rate of return for project B, then use anequation like the one in (b) to actually find the rate of return of project B. Verifythat it is consistent with the bound you found. (2 points)2. An economy is currently made up of a firm that produces bread, a firm thatproduces butter, and a consumer who consumes both bread and butter. Currentproduction is 100 units of bread, 50 units of butter which the consumed by theconsumer. If the output changed to 75 units of bread and 60 units of butter, theprofit of the butter firm would go up by $42. The profit of the bread firm would godown by $76. The consumer prefers 75 bread and 60 butter to 100 bread and 50butter. It is so much better that the consumer would pay $40 more to have 75bread and 60 butter rather than have 100 bread and 50 butter. Explain, using thedefinition, why you know it is not Pareto Efficient to have the economy produce100 bread and 50 butter. (1 point)3. A demand curve is given by the following equation: P = -4Q + 160.i) Calculate the Total Revenue when Q = 25 and when Q = 28.ii) Calculate the price elasticity of demand between Q = 25 and Q = 28.Round decimal answers to two places.Explain why the relation between the numbers in (i) and (ii) makes sense. (1points4. A firm is a monopolist and faces the following demand:qPqP01485881136676212476431128524100a) It appears the consumers will continue to pay a positive price if the quantity isgreater than 8. Explain why the monopolist will never produce a quantity above8 no matter what the costs are. (1 point)b) With the costs given below, find where a profit maximizing monopolist with thedemand above will produce and find its profit. (1 point)q1234TC ($)96105115126q5678TC ($)1391551752005. A market has a demand of P = -4Q + 540. (You may find pictures helpful, butthey are not required for full credit.)a) Assume initially that this market is in LRCE with a market supply P = 2Q + 60.Find the LRCE price and market quantity. (1 point)b) Now all the little firms that existed in the competitive market have all beenbought by a giant company. The new monopoly has a MC = -2Q + 60. Explainwhy it makes sense that the monopolist has a MR = -8Q + 540 and find themonopoly quantity and price. (1 point)