posted by Ed .
If you owned your own small hot dog shop and all you sell is hot dogs and root beer how would you go about estimating your production function and your cost function?
I would use the general form of a production function where Q=f(H,R) where both H (hotdogs) and R (rootbeer) are variable inputs in the long-run. Q=output, f=function of,
H=hotdogs, and R=rootbeer. This is the recipe to figure out how much input, in what combinations can hotdogs and rootbeer be mixed to produce maximum output and minimize cost. In the short-run either hotdogs or rootbeer usage would be fixed that
formula would be if rootbeer is fixed Q=f(H,R) = g(H). The exact mathematical form of this production function is frequently referred to as the estimable form of the production
function that is using regression analysis. Production function is the relationship of outputs to inputs is non-monetary, that is , a production relates physical inputs to physical outputs, and prices and costs are not considered.
Regression analysis can also be used to estimate cost functions. Cost depends on the
level of output being produced, as well as the prices of inputs used in production. The
math equation TC = TC(Q:h,r) where h denotes the price of a unit of hotdog and r the
price of a unit of rootbeer.
To look at estimating production function I may keep track of how many hotdogs and
rootbeers are sold each day and in what combination. I may decide to keep the number
of hotdogs constant and see what happens to rootbeers and what ulitmately occurs to
output. If I hold hotdogs constant, do I sell more or less rootbeers? If I sell more my
output goes up, if I sell less then my output goes down. Based on my findings over time,
I would be able to estimate the combination of hotdogs and rootbeers mixed to produce
the maximum output.
Now in relation to estimating cost function I am going to change my prices on rootbeer because the price has increased to make rootbeer and keep hotdog prices constant to see what occurs over time. Does the output increase because my costs have or does the output decrease. I may later decide to change the prices on
hotdogs because they are more costly to produce and keep the prices on rootbeer constant to see what occurs over time. I may look at my competition to see what they're charging and what their costs
are. Based on these observations I would be able to better estimate future sales, costs and prices. Based on the information I learn I would be able to minimize cost and maximize output.
Now, not sure if that all sounds right?
IT sounds complicated. Why are you interested in minmizing cost, and maximizing output? It is easy to minimize cost...dont buy any supplies. An to maximize output doesn't make sense to me, one can maximize output by paying folks to take the hotdogs.
I would try to maximize profit, or at least think along those lines.
I agree with the third paragraph, you need some data to estimate.
Cost will be the fixed costs, plus cost of goods, plus waste. You will have waste at the end of the day, most likely. You need some estiamte of the number of hot dogs you will sell, and the rootbeer dispensed. The question asked how will you estimate the production function and the cost function. You have a lot of words that describe other things, but I think you want to try to answer the question: how will you fill out the order blank each day for supplies? How much will you sell? How will you determine the pricing? Hot dog vendors do this all over the world each day. I suspect they guage (measure) customer demand very closely. But it does seem odd to me to try to minimize cost, or maximize output...profit is really a nice measure of efforts, and it does not always mean reducing costs, nor maximizing output.