03 Jun Question In Chapter 6 of the text and in lectur
Question
In Chapter 6 of the text and in lecture we are introduced to the concept of technology and production. Technology is the way things (goods and services) and put together and this technology embodies all of the wisdom, tools, and know-how that goes into the making of things. For example, the technology of today’s dental care (a service) includes high speed drills, pain killers, and years of study in graduate school.
The production function tells us that for a given technology, what combinations of factors of production yield us output. We say that:
X = F ( K , L ) which means that there is a functional relationship between capital, labor, and the output of “X”.
Ultimately, we will need the production function and its underlying technology to help us define the cost curves for the firm. After all, cost will be the use of factors by the firm to produce a quantity of “X” multiplied by the price paid for these factors.
From our derivation of cost structures that come form the Production Function, we can derive the supply curve for the firm – the price each firm will need to cover costs at different output levels.
The production function tells us the amounts of factors we need to produce any given quantity of a good or service. It also tells us the cheapest and most efficient way to do this. (That is, the production function tells us how X is being produced with factors of production and the best available technology.)
We use isoquants to depict the production function in a two dimensional world. Between the use of capital (K) and labor (L), the isoquant tells us at what rate the two factors must be substituted against each other to keep production at certain level. Just like the indifference curves that describe an individual’s utility function, isoquants can be seen as contour lines on a map whose position and height in the two-dimensions is determined by the underlying technology of production.
We will eventually see that in the SHORT RUN, at least one factor is fixed for the firm and its quantity used in production cannot be changed. In the LONGRUN, all factors can be changed.
Isoquants can tell us many things: they can tell the degree to which factors of production are complements, substitutes, and how for a given level of production, they can be traded at the rate of MRTS – marginal rate of technical substitution (also referred to in the textbook as the RTS). The MRTS, or slope of the isoquant is negative, it falls as you substitute one factor for another, and it is the ratio between the marginal physical
products of the individual factors.
That is: MRTS between capital (vertical axis) and labor (horizontal axis) = MPP(labor)/MPP(capital). This also can be written as MPL/MPK.
We can also show with isoquants whether or not a production function exhibits constant, increasing, or decreasing returns to scale.
So, let’s get to the homework:
(1) Is it possible for a firm to have two isoquants that cross over each other? Could a firm’s isoquant ever slope upward? Why or why not?
(2) A firm has a production function of the form Q = K (1/2)*L (1/2) where the (1/2s) are the exponents. What is the output if the firm uses 9 units of labor and 4 units of capital? If the firm doubles its input levels, what happens to the level of output? Does this firm’s production function exhibit constant, increasing, or decreasing returns to scale?
(3) Let’s assume that your GOAL is to maximize your “output” that you define as getting an “A” course grade in ECN 100 at UCD. How would you go about constructing a production function (the inputs) that would help you achieve this result? How would each of the factors relate to the desired output? How would you go about assessing the marginal productivity of each of the factors of “production” in this case?
Okay – now chose one of your factors of production that is an input to the getting of the a grade as THE MOST IMPORTANT FACTOR, and state how the available level of technology would affect its role as an input to the desire output, X = grade.
(4) Do you realize that you have your OWN PERSONAL production function?
The value or ability of whatever you produce is a function of the various inputs that you put to productive use working with your body and mind. Now, think of an important output goal you would like to achieve (like getting a Law Degree or becoming a bicycle racer, or whatever) and devise an “input” strategy to reach this goal in an effective manner. Once you decide on these inputs, how do you think the current level of Technology helps determine how these inputs will work in your efforts to produce an output result? This is an important problem and we will also discuss it in lecture.
(5) What might be the three most important inputs to the following production activities?
The manufacture of Honda Civics
The growing of organic lettuce
Nordstrom Department Store
Your ability to do math problems
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