Jul 14, 1984 - search for price information include Landsberger and Peled, Telser, Goldman and. Johansson, Russo, Alcaly, and Devine and Marion. Others ...
staff Papers series S’I’AIV? PAPER I?84-14
JULY 1984
HOG PRICES RECEIVED ANI)THE VALUE O“FINI?ORMATION: A LOGXT ANALYSIS
Hannelore Baumaqn and Jean Kinsey
lD@patimentof
Agricultural
and
Bpplied
Universityof Minnesota Institute of Agriculture, Forestryand Home St. Pad, Minnesota 55108
Economics
Economics
Hog Prices Received and the Value of Information: A Logit Analysis
tlanneloreBaumann Jean Kinsey*
July 1984
*
Hannelore Baumann is a Research Fellow and Jean Kinsey is an Associate Professor in the Department of Agricultural and Applied Economics, University of Minnesota, St. Paul, Minnesota. Staff papers are published without formal review within the Department of Agricultural and Applied Economics.
/
Hog Prices Received and the Value of Information: A LogiJ Analysis
The economics of imperfect information has captured the imagination of numerous economists. Stigler’s seminal article pointed out the often quoted result that information is sought until the value”of its last unit equals the marginal cost of obtaining it.
Several authors have subsequently studied
consumer’s information search process including Gastwirth, Milde, Nelson, Hey, Lamouroux, Schwartz and Wilde, Manning and Morgan, Karni and Schwartz, Braverman, and Burdett and Malueg. Researchers who have studied primarily the search for price information include Landsberger and Peled, Telser, Goldman and Johansson, Russo, Alcaly, and Devine and Marion. Others such as Colantoni et. al. have concentrated on information about product quality. Kinsey, Roe, and Senauer integrated imperfect information into consumer utility theory. The study discussed in this paper integrates the economics of information, production theory, and the theory of human capital to determine the optimum amount of price information collected by profit maximizing hog producers. Increased use of price information is believed to increase profits but questions about the actual profitability of acquiring and using information as a production factor are unanswered in much agricultural research, One of the reasons for neglecting this area of research may be the scarcity of cross-sectionaldata on information use. Theory predicts that a profit maximizing hog producer would seek information until the value of the marginal product of an additional unit of information ceases to exceed its marginal cost. That marginal cost is determined largely by the opportunity costs of farmers’ time which is, in turn, determined by the amount of human capital invested in the farmer. Studies by Schultz, Mincer
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and Ghez and Becker describe the positive effects of investment in schooling, . health-and other human capital enhancers on income and wage rates and hence on the value of time. Considering price information as a variable input into the production and marketing of hogs, a profit maximizing production model was used in this study to determine the optimum amount of information for farmers with varying investments in human capital. ‘ A description of the data collected specifically to study the impact of farmers’ human capital on the use and profitability of information appears next. The theoretical model is presented followed by a methodology section which develops the logit estimating equations. A discussion of the findings of three different model specificationsreveals generally similar results. The .theoretically derived-hypothesesare confirmed for the sample of hog farmers used in this study.
Data Sources For thi% study a survey was conducted in one of the most important centers of hog production in Germany, namely Northern West Germany. Confining the survey to a region where hog producers are highly specialized eliminated regional price differences, and contributed to the homogeneity of the sample. That is, farm size or the quantity of hogs sold by individual producers can be assumed not to have influenced the received hog price. These farmers produced an average of 900 slaughter hogs per year per farm. Farmers reported their use of hog price information and the prices they received for hogs. The price of slaughtered hogs within the EEC is not a guaranteed price. Therefore, one would expect to find highly specialized hog producers with a homogeneous product to be receiving various prices mainly because their management abilities vary and depend on their education, experience and information use.
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Data was gathered via written questionnaires distributed to 665 hog farmers .-by 40 county agents in the specified region. Three hundred and eighty two completed questionnaireswere collected for a response rate of 57 percent. Besides questions about the price farmers received for slaughtered hogs, there were questions about the farmer’s age, level of education, including education in agriculture, the number of years operating the farm, and their use of various sources of price information
On the basis of the survey data the effect of
price information and human capital factors on prices received for hogs could be estimated.
Theoretical Model The central idea of the human capital theory is that lifetime earnings depend on formal and informal education including experience, The costs of increased formal education include not only direct costs such as tuition and other school related expenditures but the value of earnings foregone while one is being educated. The costs of informal education include direct outlays for printed material, equipment or travel as well as opportunity costs equivalent to the value of time which could have been used in other activities. For hog farmers, the opportunity cost of the time spent searching farm magazines or newspapers for hog price information is the value of alternative activities that might also increase their income and/or their utility. The theoretical model predicts that profit maximizing farmers will search for current price information until the value of the marginal product of information equals the factor price of information. Assuming a farm magazine or newspaper would be purchased whether or not it was were used for hog price information, the direct costs of purchasing newspapers and farm magazines can be
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the farmer’s opportunity cost of ignored and the price of information becomes . time as measured by the wage rate. The model presented below illustrates this simple result after showing how the demand for information is decreased by increased formal education. The result depends on those with more formal education being more productive at all input levels. The formally educated were assumed to process ‘informationmore efficiently and therefore, to use less information for a given level of production. Education and information became substitutes. Education acts to shift the production function. The supply of hogs for sale is a function of their output price, factor input prices, education and experience. .- . 1)
H = h(PH, WB; E) H is supply of hogs produced for sale PH is the price received for hogs ‘H
is the full coet of producing and marketing hogs
E is education and experience. 2)
‘H
= rk~+
~r x. + rtt ~jJ
where the r’s are the factor prices, ~
k#j
is the quantity of information used in
producing and selling hogs, the x ‘s are other variable inputs and t is time. j Assuming that the only cost of gathering price information is the cost of the farmer’s time, rk = rt = wage rate. Following the procedure detailed by Robert T. Michael (pp. 94-95) for looking at the impact of education on household production we find that holding inputs constant and collapsing all x’s into one vector (xi), the production function and the change in production due to education is depicted by equations
.,
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(3)alld (4). Converting (4) to a percentage and dividing through by ‘Hshows . 3)
H=xMP k%+twt atw
4)
Q&
=MPH=xk(
dE[ X,t
---% ak
+ , (~) a~
that”the percentage change in the marginal productivity of hog production due to education (MPh) equals the weighted sum of the percentage changes in the marginal productivities of factor inputs due to education (&@x ). -.~ J-,L
5)
* Ml?H=~ WXMFX+wtMFt iii
where N designates the percentage change due to education, Wv is the weight ‘ii,t of’each factor of production. For example, ht = tMPt/H, the proportion of hog ,production determined by the input of time. Alternatively, allowing factor quantities to change with education results in the percentage change in hogs produced equaling the weighted sum of the percentage changes in factor inputs.
6)
I=lW ;.+wt: x. 1 il
In equation (5) education affected hog production through its impact on productivity whereas equation (b) shows the indirect effect of E on H through induced changes in quantities of inputs. The effect of education on the full cost of producing and selling hogs is evaluated as follows with H and ri held constant.
To evaluate the effect of education on the quantity of inputs (dxi/dE), equations 5 and 6 are summed, set equal to zero, and solved for xi. Since the
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information input (xk) is of particular interest in this paper the change in its quantity will be derived to illustrate the effects”of education on its use. Summing equations (5) and (6) and solving for ‘~ yields (8a, b).
Substituting from (5) for - l&H and consolidating,yields
~ O, which_means that the % first term on the right hand side (rhs) of (9) is zero or negative. If educa-
For the sample being studied it is assumed that @
tion increases the marginal productivity of time and decreases the amount of time that is spent for a given H, the second term on the rhs is also negative. Whether education changes the ~fi and ~~. is indetermin~te but it is generally j ‘j j’ expected that the signs will be positive and negative respectively. On balance .-
‘k should be negative -- less information will be sought by those with more education. How does this result affect the profitability of hog farmers and their returns from information search? The purpose of searching for hog price information is to alter the price received for hogs. The farmer is still a price taker but can adjust profits by timing the sale of hogs to correspondwith the best market price available. The relevant profit maximizing criteria is to equate the factor input price (rk) to the value of the marginal product (VMP).
. .
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10a) Profits = 0 = H.pH- (rkxk + ~rjxj ‘,rtt) - F ~--j where I’h= f(xk), F are fixed costs. lob) 6 = Hf(xk) - (rkxk+ ~r.x. + rtc) - F jJ3 Maximizing 6 with respect to Xk yields J& ha) d%
af(xk)
= li[=
) - rk= O
af(xk) —) llb) H(a %
.rk
llc) VMP = rk = wage rate by assumption rk = rt = wage rate, therefore, the .yalueof the marginal product of information is equal to the wage rate. Farmers will seek information on hog prices until the value of the last price sought equals their wage rate. Figure 1 illustrates the theoretical linkages between equations (4), (9) and (llc). Panel a shows the generally high-erproduction achievable by more formally educated farmers. Since information is not the only input into hog production the functions need not start at zero. It can be seen that for a given level of hog production (h*) the educated need to use less information than the uneducated, (x;
