Question

Q1. As you have learned in the course, two main forces that lead to spatial concentration of jobs are scale economics and agglomeration economics. This question is a reminder of economics of scale from your Mi- croeconomics course. Please note this question has 3 parts. Part A: Suppose a firm at the first stage has employed 4 labors and 16 capitals. At the second stage, the manager cannot hire or fire any of the labors and cannot buy or sell any amount of capital. He just noods to decide on how many plants to build and then allocate the labors and capital among different plants of his firm equally. If you need, assume that the price of the firm's product is 1, the labor wage is w and the rental price of capital is r. Suppose the production function in each plant is given by Y-K12, where Y, K, and I denote production, capital, and labor, respectively. (i) The Production Function exhibits (choose one) (1) Increasing Returns to Scale (2) Decreasing Returns to Scale (3) Constant Returns to Scalo (4) None of the above. (2 points) (ii) Denote the number of plants by N, construct the profit maximization problem of the firm and discuss the optimal number of plants nooded to build. Asume building any extra plant has no cost for the firm. (6 points) Part B: Now, suppose the production function in Y - K ..? and everything else is the same as in part A (1) The Production Function exhibits (choose one) (1) Increasing Returns to Scale (2) Decreasing Returns to Scale (3) Constant Returns to Scale (4) None of the above. (2 points) (ii) Denote the number of plants by N, construct the profit maximization problem of the firm and discuss the optimal number of plants needed to build. Assume building any extra plant has no cost for the firm. (6 points)

Answer 1

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