Reference no: EM132321006

Case Study: Short-run Production

Please address the following case study relating to short-run production for an engineering firm. This case study relates to Chapter 8 of the textbook and the lecture on Short-run Production.

Note: The lecture is decomposed into four sections that correspond to a section of the case study and related pages of the book. The lecture section and book pages are indicated with each section of the case study.

Please submit your work as a single Word document. When I request calculations, you can write them by hand and incorporate a photograph into the document or you can type up the calculations in the document. Similarly, you can create any tables by hand, in Word, or other ways, but your tables should be clear. The document should be approximately 2-4 pages (counting each side of the paper as a page) in length. Please indicate in some way which part of the document responds to each question. The assignment will be graded based on correctness, effort, and presentation.

This table will be used in Section 2:

		Number of Prototyping Facilities (K)
		0	1	2	3	4	5
Number of Engineers (L)	0	0	0	0	0	0	0
	10	0	1.4	2.4	3.1	3.6	4.1
	20	0	3.3	5.7	7.4	8.7	9.9
	30	0	4.6	8	10.4	12.3	13.9
	40	0	5.8	10	12.9	15.2	17.3
	50	0	6.8	11.7	15.1	17.9	20.3
	60	0	7.7	13.3	17.1	20.3	23
	70	0	8.5	14.7	19	22.5	25.5
	80	0	9.3	16.1	20.7	24.5	27.8
	90	0	10	17.4	22.4	26.5	30.1

Section 1 - Types of Costs and the Basics

a) Houses can be made from brick, wood, or a combination of brick and wood. It takes 60 pieces of wood or 20 pallets of bricks to make a house. (You can also substitute a pallet of bricks for 3 pieces of wood etc.) Assuming wood and bricks are the relevant inputs to a house; write down a production function for houses.

b) The seat for a new car can be designed with either of 2 technically efficient combinations of inputs: either (30 engineers and 3 prototyping facilities) or (35 engineers and 2 prototyping facilities). Engineers cost $100,000 and prototyping facilities cost $1,000,000. Which combination of inputs is economically efficient?

Section 2 - Production in the Short-run

a) The table on the first page depicts the quantity of engine parts designed by an engineering firm using different combinations of engineers (L) and prototyping facilities (K). Using the table and holding the number of prototyping facilities (K) fixed at 3, complete the following table. Note that labor increases in 10 unit increments which will be relevant when calculating the marginal product.

L	Q	AP	MP
0
10
20
30
40
50
60
70
80
90

b) At what point in this production process do we start to notice diminishing marginal product?

c) Create a graph showing the relationship between the number of engineers (L) and output.

d) Create a graph showing the relationship between the number of engineers and average product as well as marginal product.

Section 3 - Short-run Costs of Production

a) Identify whether each of the following costs is an explicit cost or an implicit cost as well as whether each cost is a fixed cost or variable cost and finally whether each is a sunk cost or avoidable cost and briefly justify your answer. (There may not be a perfect answer.)

i. The prototyping facility needs plastics and metals to create parts.

ii. You use 100 square feet in your firm's headquarters for each of your engineers.

iii. You purchase a single non-transferrable, unlimited-user site license for your Computer-Aided-Design software.

iv. Each engineer needs a computer that must be destroyed when he is done to prevent its contents from being searched.

v. A law firm is hired to secure a long-term contract with a larger firm.

vi. Your firm's lawyers are used to write a long-term contract with a larger firm.

b) Assume as you did in the beginning that each engineer costs $100,000 and are a variable input while each prototyping facilities costs $1,000,000 and three of them are fixed inputs. Use the table you made in Section 2 to help complete the following table (round to the nearest dollar when necessary):

Q	FC	VC	TC	AFC	AVC	ATC	SMC
0
3.1
7.4
10.4
12.9
15.1
17.1
19
20.7
22.4

c) Use the table you completed to construct a graph depicting the AFC, AVC, ATC, and SMC for engine parts in this setting. Please title and label the axes and be at least somewhat precise in your drawing.

Section 4 - Relationships Between Production and Cost in the Short-run

a) What is the relationship between AVC and AP in our setting? (You should plug in for the wage.)

b) What is the relationship between SMC and MP in our setting? (You should plug in for the wage.)