J.-F. Gautrin and B. Verdon

pp. 3–26

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Abstract
This paper deals with a macro-simulation and forecasting model, called PASSIM, essentially markovian, of the working of the Quebec system of Public Assistance. It has to do with both the numbers of persons involved and with the expenditures. It became fully operational in the summer of 1972 albeit it still contains a number of important imperfections.The model relies on a linear programming procedure to estimate probability transition matrices. This seems to represent one of the original features of the model. The basic philosophy of the Quebec Public Assistance is simple: a modified version of a guaranteed income program. This needs test is simply used to constitute the submodel for the determination of allowances. Transition matrices are three dimensional; transition probabilities may change over time due to changes in various exogeneous variables.The model is particularly oriented to test some major changes in the law. An example of a typical simulation is presented and some gross sensitivity tests are also given.

Neil Swan

pp. 27–46

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Abstract
The paper develops a formal theoretical model of expenditures for a typical Canadian provincial government. The model is kept simple but useful by restricting the endogenous variables to four important budgetary categories: highway spending, hospital care expenditures, spending on schools and universities, and "all other" spending. Tax rates are also endogenous to the system. The choice of these four expenditure categories is linked to the original motivation for the model, which was to assist in explaining provincial construction spending. The theory has three elements: first, a utility function, which depends positively on the amounts provided of government services of various kinds, as well as on the income left to the public after taxes and borrowing; second, a budget constraint linking expenditures and revenues; and finally, a set of equations which show how much spending is required in order to provide the quantities of services entering as arguments into the utility function.The reduced form model developed from the theory is then fitted to expenditures data for each of the ten provinces over the 1952-1970 period. Fits are generally good. Tax equations, though not presented here, also fitted well. Provincial income levels, beginning year stocks of structures, rates of matching grants, construction prices and the closeness of elections are the main exogenous variables that prove important in explaining per capita expenditures within each of the four budgetary categories.

Ruth Rose Parker

pp. 47–62

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Abstract
This linear programming model for educational planning, by allowing for choice among techniques of production, permits the introduction of non-constant factor substitution into the production function. The model is applied to educational planning in France and treats simultaneously four kinds of educated manpower and capital in the seven major industrial sectors of an economy. Alternative techniques are drawn from seven other countries for which reasonably comparable data are available. These techniques of production define the production function and determine the demand for educated manpower and capital independently of the supply of these factors.An initial static model maximizes GNP (holding its composition constant) subject to a fixed supply of manpower and capital. The model thus tests whether supply is the constraining factor in the choice of technique in theshort run. In the case tested, it is.In the dynamic version of the model, supply is allowed to increase by means of education (for manpower) and investment (for physical capital). Consumable GNP, that is GNP net of the cost of education and investment, is maximized. Terminal capital stock problems make it impossible to test the model directly. The problem is then broken down into two steps: the identification of the techniques (one for each industry) which permit the greatest net contribution to GNP, and the movement in time towards these "optimal" techniques. The first of these steps is solved using a dual version of the model, but the second is not attempted in this paper.

Michel Boucher

pp. 63–78

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Abstract
The focus of this article is to analyse the reasons for the success of the Québec Lotteries. To do it perfectly, we study the technical terms of the lottery, drawing, namely the expected value, the probability of winning a prize and the inequality of the prize distribution. Then we analyse some changes introduced by Loto-Québec and we contrast the results with other more established lotteries and the differences so observed may provide additional reasons for its success.In the second part, we use the theory of choice involving risk as described by Allais and Tobin to explain the demand for lotteries tickets. We find, by a statistical analysis, where the independent variables are the mean value and the variance of the prize distribution, that people who buy tickets are generally speaking risk-averters and not risk-lovers and they behave as such when Loto-Québec changes the mean value and the variance.