1. Assume there is a market with 2 firms, producing goods z and m. Labor is the only input in production of each good. That is, I; is labor used to produce good z and I is labor used to produce good m. The production of z is given by the function: z=16 /%2 The production of m is given by the function: m =16 |42 2. Suppose the price of the outputs, both z and m, is 1, and the price of labor for both z and mis $10. a. Derive the conditions that characterize the socially efficient outcome. You DO NOT need to solve explicitly for I:and Im, just derive conditions describing the efficient outcome. Note that this is not exactly like the model discussed in class, 50 use the basic ideas rather than the specific approach to set it up and solve it. HINT: Use the production functions to write the objective function as a function of I: and Im only. 3 points b. Derive the conditions that characterize the market outcome. 3 points c. Show that if there is no externality, the market outcome (b.) and the efficient outcome (a.) are the same. 2 points d. Show that if there is a negative externality, too much labor is hired in production of z and too much z is produced, but the output of m is efficient. 3 points e. How does your answer to (d.) change if there is a positive externality? Explain and show algebraically. 3 points 1. Recall the externality problem from Problem Set #1: there are 2 firms, producing goods z & m. The production of z is given by z =16 /1,2 where I, is labor used to produce z. The production of m is given by m = 16 In'?2 where I, is labor used to produce m. The price of the outputs, both z and m, is 51, and the price of labor for both z and m is $10. Suppose there is a negative externality (6