Suggestions for problem set 4
The main themes in this problem set concern the nature of production in the short run, the implications of the nature of short-run production for the shape of the various firm short-run cost curves, and the significance of the firm short-run cost curves for short-run supply decisions.
First, it is important to understand the distinction between the short run and long run. A production function for a good describes how the quantity produced of the good is related to the quantity employed in production of various inputs to the good. There is always a time dimension to production. Although it is often left implicit, a production function describes how much output of a good can be produced in a specific time period, such as a month, as the quantity of inputs to the good are varied within that time period. Depending on the time period considered, it may not be possible to vary all inputs. For example, in the production function describing the quantity of automobiles that could be produced in the next month, the production period would not be long enough to build a new factory to produce automobiles. Therefore, the total factory space devoted to automobile production in the next month could not be varied—it would be considered a fixed input. Production is described as being in the short run when the time interval for production is too short to vary all inputs, so that some inputs are fixed. The reading for this problem set in the textbook describes the nature of production in the short run.
There is a lot of terminology in the readings for this problem set. It is very important to master it and to understand its significance. The first part of the reading deals with production and introduces the concepts of total, marginal, and average physical product. It goes on to discuss the Law of Diminishing Returns and the Three Stages of Production. Problem 1 involves computing the marginal (physical) product schedule based on the production schedule in table 1 before and after the reorganization of the hypothetical firm in the problem (the word physical is commonly omitted from references to the total, marginal, and average physical products). You should be able to do this simply by following the discussion on page 115 of the textbook.
Problems 2-5 all involve the various firm cost schedules, including the total cost schedule, total variable cost schedule, the marginal cost schedule, the average fixed cost schedule, average variable cost schedule, and average total cost schedule. The relationship between these cost schedules and the total, marginal, and average physical product schedules is developed on pages 139-143 of the text. It is essential that you be facile with all these different cost schedules, as they play a very important role in supply decisions. Going from the physical product schedules to the cost schedules requires putting a value on inputs used in production. This is discussed on page 136 of the textbook under the topic, "The Classification of Costs." Problem 2 involves an application of this discussion. If you win a new house in a lottery, do you incur a cost in occupying it? Is there an opportunity cost to occupying it and thus an implicit cost to occupying it? You should consider this issue in answering problem 2.
Problem 3 exercises your understanding of the various cost schedules. You are given the total cost schedule of a firm. The total cost schedule does not distinguish between fixed costs and variable costs. How can you infer the total fixed costs of production from the schedule? (Fixed costs are incurred regardless of the level of output produced and thus are incurred even if the firm produces no output.) Once you have inferred total fixed costs, how can you extract the total variable cost schedule, which indicates the total variable cost of producing each level of output? Once you have extracted the total variable cost schedule, increase the total variable cost by 25% at every level of output, so that you have the original and new total variable cost schedules. Parts a-e of this problem can be answered by computing the relevant average and marginal cost schedules from these two total variable cost schedules. Part f also requires computing the average total cost schedule, which can be computed from the total cost schedule after the increase in variable costs. How can you compute the total cost schedule after the increase in variable costs if you have the total variable cost schedule after the increase in variable costs and you know the total fixed cost? It is important that you do all computations on your own and do not copy anything from the solution set. By doing the computations, you should develop a deeper understanding of the various cost schedules and how they are affected by a percentage change in total variable costs at every level of output. You can test your understanding of the relevant concepts on Quiz 4, which involves the same issues as this problem.
Problem 4 involves further computation of the various cost schedules. Parts d and e raise a new question, namely given a price, how much should the firm supply if it wants to maximize its profits. The basis for this decision is discussed on pages 144-146 and 152-154 of the textbook. This is an extremely important topic and one that is not easy to understand. Review these pages carefully. What schedule is relevant to the question of how much the firm should supply? How does the textbook indicate this schedule should be employed to determine the profit-maximizing level of output? You always need to check that the firm would be better off producing this level of output than simply shutting down and earning losses equal to the total fixed costs of production (which it must incur in the short run even if it shuts down and produces no output). Review the discussion on page 154 concerning the price required to induce the firm to produce a positive level of output in the short run (i.e., when the firm incurs fixed costs even if it produces nothing). Is the price high enough in part d to justify the firm supplying a positive level of output? Part e of problem 4 poses a licensing fee and asks how the licensing fee affects the profit-maximizing level of supply assuming the price is unchanged. To analyze this, consider how the licensing fee affects the key schedule that determines the profit-maximizing level of output and how it affects whether the firm might be better off shutting down entirely rather than supplying a positive level of output.
Problem 5 probes your understanding of the distinction between fixed and variable costs and how these in turn are related to the various average and marginal cost schedules. It is a good test of how well you understand the various cost curves. If you have difficulty with this problem, go back and review the various cost schedules.