HELP ME PLEASE

\fe.) Suppose you are a rm that introduces a new good into the marketJ let's call it good L + 1. Suppose the characteristics of your novel good are described by the vector {01'1"}.11 ...1 \"LI-+1 :1, for which each component is strictly positive. 'What. price do you want to charge the consumer per unit of the new goo-d? 4. llilonsider an Lgood economy in which every consumer has a strictly positive initial endowment of every good and has a concave utility function that depends only on what that consumer consumes of the L goods Suppose rst that no production is possible. a [s a competitive {Walrasian} equilibrium allocation in this economy necessarily Pareto optimal [Pareto elcient}? Be sure to assume only what is given above. Use an Edge- worth box to justify your answer. b. [s every Pareto optimal allocation necessarily part of a competitive equihbum with the given endcrltl'rnents'i| Now assume that production is pomible in this economy. c. Suppose that good 1 can be produced using good '2 as input, but that good 2 cannot be produced. Show that it is possible that the economy has no competitive equilibrium. Explain how it is pomible. d. Suppose instead that o units of input of good 2 produce q units of output of good 1 for any 11 2 I]. Also, suppose that 1; units of input of good I produce as units of output of good 2. In order [or competitive equilibrium to exist, what restriction must no satisfy? Explain. e. Suppose that, under the assumptions of part d, the economy has a competitive equilibrium in which a positive amount of good 1 is produced using only good 2 as input. What can be concluded about the relative prices of goods 1 and '2 in equilibrium? Be as specic as possible and show that your answer is correct. f. 1|n'uu'hat prot does a producer of good 1 receive in the equilibrium of part e? [s the total prot of the producers of good 1 in that equilibrium a good measure of the benet the consumers in the economy get from the presence of the technology that transforms good 2 into good 1? Explain