Get Valid Answers To These Thought-Provoking Questions On Economists Production Theories
What is Production?
What does the economist Production Decision entail?
- The input budget.
- How much of each input to purchase.
- Allocation of inputs to different outputs.
- How much of each output to produce.
How Do Production Costs Behave?
- the market period when output cannot be changed, and the given stock has to be cleared from the market by lower prices or stored.
- In the short run, when at least one input, usually the capital, cannot be varied.
- the long run, when the inputs can all be varied.
- In the very long run, when available technologies change.
Explain factors affecting Economies of scale and how it affects fixed and variable costs
Fig. 14.1 How Fixed cost Vary with Output
Fig. 14.2 How Variable cost vary with Output
Fig. 14.3 calculating the marginal Product of Labor
What is a Production Function?
Expressing the relationship between input and output in mathematical terms is called a production function. They differ in both their origin and their nature.
One important function for production has been the attempt to find a function that would reproduce such phenomena as diminishing returns of economies of scale. We call these 'theoretical functions because they have the theory first. They can be for either a firm or an industry (sometimes termed Marshallian functions after Alfred Marshall) or the economy as a whole (Walrasian after Leon Walras).
Another possible origin is in empirical investigations, seeking to find relationships between inputs and output from studying masses of data. This tends to run up against the statistical and practical problems mentioned in Chapter 13.
Perhaps the most obvious source of production functions has proved somewhat disappointing, the study of engineering data. The one area where it has proved useful is in establishing whether economies of scale exist in various industries.
State and explain the Marginalist and linear functions
Production functions can almost all be divided up into those which are marginalist and those which are linear. Chapter 15 deals with the two approaches' main strengths and weaknesses and gives insight into their development. The next section shows how a function might be developed from known data and then used for production costs (purchasing costs in this case).
The Stockholding Model
A problem faced by all firms is the right level of stocks of finished goods to hold. With perishable (ii) w products, it seems obvious that there is an upper limit to sensible stockholding, the amount that could be sold when it takes the product to decay. Other products could be kept for a year before they became out-of-date, so they lost their value. Can we elucidate any general principles?
The first insight we can gain is that this is a typical economic problem; higher stocks mean es likelihood of being out-of-stock but costing more to store. If we remove uncertainty about demand and thus turn the problem into one of certainty, do we still have the incentive to hold large stocks? The answer is yes because if we order every week, the os will rise, both orderings costs themselves and, probably, transport costs. Ordering every week will mean smaller stockholding costs than large ordering costs; ordering once a year will mean small but large stockholding costs. We can build a cost model as in Figure 14.1. As we know from previous experience, there are two main ways of handling problems of this kind once we have a model. Simulation and use of mathematical properties ('analytical methods). Let us see how they work in this case, and see which is best.
Simulating different stock levels
We can assume that the firm will know with certainty its various costs and the annual level of sales. It is then just a matter of substituting different values of D into the equation from Table 14.1
Table 14.1 Building a stock holding cost model
|(i) Q/D = Number of orders/year where
D = delivery size
Q = Annual Sales
W = Storage cost per unit stored
|(ii) D/2 = average stockholding
a = fixed order cost
b = per unit order cost
|(iii) W x D/2 = Total Storage Cost
|(iv) A + b x D = cost per order
(v) Total Cost = Total Storage Cost +Total Ordering Cost
+ (i) x (v)
+ Q/D x [a + bD]
+aQ/D + bDQ/D
+aQ/D + bQ
Normally w, Q, a, and b will be known, so varying D varies TC
Table14.2 Calculation for stockholding simulation
|TC=WD/2 +aQ/D + bQ = TC
|100/2+1000+2000 = 3050
|200/2+500+2000 = 2600
|a = 100
|300/2+333+2000 = 2483
|300/2+333+2000 = 2483
|500/2+200+2000 = 2450
|600/2+167+2000 = 2467
|700/2+140+2000 = 2490
Table 14.3 Analytical method of minimizing stock costs
|The formula is TC=WD/2 + aQ/D + b
It is easier to differentiate as TC = WD/2 + aQD-1 + bQ
Differentiating dTC/dD=W/2- aQD-2 =(0 when TC is minimized)
Thus at minimum, TC w/2 = aQD-2
As D -2 = 1/D2 then W/2 = aQ/D2
Multiplying gives WD2 = 2aQ
Dividing gives D2 = 2aQ/w
Taking the square roots D= 2aQ/W
When TC is minimized
Produce the calculations in Table 14.2 and the graph in Figure 14.4. The graph clearly shows the value of D that will minimize the cost of holding stock to meet an annual demand of 1000.
Provide an analytical solution to the cost
Those who know some calculus will recognize that we have an expression for TC in which D is the only variable (in any particular case, a, b., Q and W will be constants above in Table 14.2). Thus we can say that TC will be minimized.
Let us explore the first condition: taking setting it = to 0.
Readers might like to check that the derivative is positive; the t has been minimized at the value for the D-found process. If we substitute the values for a,b, and a that we used in the example in Table 142 veg, a value for D of about 447. This agrees with a simulation that puts the lowest TC at a value of d between 400 and 500.
Thus both methods provide the same, but this example shows a clear advantage. T analytical method can be applied to any value a. b. W and without having to go through a simulation each time. One of the crucial judgments that managerial economists have to make is when a standard analytical formula can be applied and when a simulation model has to be created. One of the exercises explores the analytical formula further.
Chapter 15 looks at two more production functions where mathematical analysis has provided some interesting and rewarding might production decision-making.
Fig. 14.4 graph of stockholding simulation
Key Concepts - Review
Long run/Short run
Marginal product (of Labor)
Diminishing returns (to an input)
Returns to scale
Economics of scale
Provide a Case Study on This Report
You work for an electricity meter manufacturer which operates on a government trading estate on the Welsh border. All the meters are brought in from Japan, recalibrated by skilled workers, and then sold to the Midlands Electricity Board, your sole customer. The firm employs nine people and has a turnover of 72,000 meters yearly for gross revenue of 120,000. The cost breakdown is as follows:
|Wages and Salaries
|Factory (rent, rates, heating, and lighting)
You have been concerned over the space taken up by stocks for some time. The finished goods are no problem; they are sent off every Thursday to Birmingham, and the lading bay w store a week's output. However, the Japanese meters come in at 18.000 at a time every three months, and half the factory space is taken up storing them. As the trading estate company only charges you for the space used, you are eager to find ways of reducing thin storage space.
The original reason for only buying every Three months was the cheaper price of a large order. You have learned that the Japanese quantity counts are based on a fused charge of $1.00 and $1.90 per meter. Your 18.000 meters cost $2 each, but if you bought every month, the 6000 meters would cost you $2.60 each.
However, a fresh complication has arisen: your boss has got an order for 1000 meters a week from the Yorkshire Electricity Board. The extra 13.000 meters needed each quarter would mean even more storage space would be needed. The trading estate has space available, and you work out t would cost about the same per square foot as your present space.
The boss wants to know whether to rent more space and whether to change the size, frequency of orders, or both. You remember seeing how the problem can be solved in a managerial economic book but are suspicious of the magic formula. You decide to work out for yourself the best size of the order, doing it in two stages, first the best order size for the present output and then the best order size, including the Yorkshire contract.