In the Percent Over Last Year method, the projection is based on data from the same time period in the previous year. When specified in the processing option, the forecast is also adjusted for seasonality. This is represented by the point 6,0 on the graph. The basic calculation in the sales budget is to itemize the number of unit sales expected in one row, and then list the average expected unit price in the next row, with the total revenues appearing in a third row. Question 5: Recall that the indifference curves are L-shaped blue in the graph and have a kink at the 45° axis, as indicated in the graph. If José had unlimited income or if goods were free, then he could consume without limit.
One application of linear equations is illustrated in finding the time it takes for two cars moving toward each other at different speeds to reach the same point. This is a little weird since the slope is usually defined as the change in y divided by change in x, so be sure not to get it backward! Real-life examples of linear equations include distance and rate problems, pricing problems, calculating dimensions and mixing different percentages of solutions. Formally, this can shown as follows c. In a two commodity model, the budgetary constraint can be expressed in the form of the budget equation: P x. Recall that the government should spend the same amount of money in both cases. Those two points define a straight trend line that is projected into the future. Alternately, Budget Line is locus of different combinations of the two goods which the consumer consumes and which cost exactly his income.
In some cases, it is convenient to consider the loss due to distance and wavelength separately, but in that case, it is important to keep track of which units are being used, as each choice involves a differing constant offset. Long distance became practical only with the development of ultra-transparent glass fibers. A forecasting method that is appropriate for one product may not be appropriate for another product. For example, when a new product moves from introduction to growth stages, the sales trend may accelerate. Budget Set : Budget set is the set of all possible combinations of the two goods which a consumer can afford, given his income and prices in the market. Remember, the slope is the rate of change.
Each forecasting method will probably create a slightly different projection. Note that any point within the budget line is feasible. For example, the weight placed on recent historical data or the date range of historical data used in the calculations might be specified. Conclusion Though we understand the different ways by which consumers can exhaust their income, we have not yet discussed how to determine which bundles of goods different consumers prefer. It is generally best not to include in the sales budget any estimates for sales related to prospective acquisitions of other companies, since the timing and amounts of these sales are too difficult to estimate. This means that not spending his full budget is essentially wasted income. A Higher Interest Rate When the interest rate increases, the opportunity cost of consumption increases.
The easy answer to this question is to find out how much the income has increased by, and multiply the total amount of goods consumable by the same amount. We know that the higher the indifference curve, the higher is the utility, and thus, utility maximizing consumer will strive to reach the highest possible Indifference curve. All income is spent on goods that increase satisfaction. This means that the highest possible indifference curve that you can be on is the one that is just touching or tangent in one place only to the budget constraint assuming, that is, that the indifference curves are strictly convex. Note that the indifference curves are red and the budget line is blue in the graph. Required sales history: The number of periods to include in regression processing option 5a , plus 1 plus the number of time periods for evaluating forecast performance processing option 19.
Linear regression fits a straight line to the data, even when the data is seasonal or would better be described by a curve. Back to the Facts Spending patterns are interpreted as revealing the best choices households can make, given their preferences, income, and the pr ices of the goods they consume. The engineering and marketing managers may also contribute information about the introduction date of new products, as well as the retirement date of old products. However, for analysis, absolute value is always considered. This recommendation is specific to each product, and may change from one forecast generation to the next. By The key to moving from unconstrained optimization to constrained optimization is the introduction of a budget constraint. Here, José buys 4 T-shirts and 0 movies.
Then, putting these values in 6. Now, the consumer has three options to spend his entire income: i Buy 2 units of X; ii Buy 2 units of Y; or iii Buy 1 unit of X and 1 unit of Y. As we saw above, as price doubles, the quantity the consumer could previously purchase is halved. These effects are implicit in the income and substitution effects we will explore shortly. This method works better for short range forecasts of mature products rather than for products in the growth or obsolescence stages of the life cycle. Required sales history: Twice the number of periods to be included in the average processing option 4a , plus number of time periods for evaluating forecast performance processing option 19. Both of these performance evaluation methods require historical sales data for a user specified period of time.
The data in this period is used as the basis for recommending which of the forecasting methods to use in making the next forecast projection. The price ratio of 2 means that José must give up 2 movies for every T-shirt. If this is done, the rest of the budget that is derived from the sales figures will also have to be revised, which can require a significant amount of staff time. This means that there is always a crossover distance beyond which the loss in a guided medium will exceed that of a line-of-sight path of the same length. . When the sales history data follows a curve or has a strong seasonal pattern, forecast bias and systematic errors occur. It means, a consumer can purchase only those combinations bundles of goods, which cost less than or equal to his income.
José now has access to some new consumption opportunities, but many others are now unavailable. Valid values for a range from 0 to 1, and usually fall between 0. The information in the sales budget comes from a variety of sources. The intersection between this line and the budget line is the optimal consumption choice. Important Points about Budget line Refer Fig. During the Neptune flyby, in addition to the 70-m antenna, two 34-m antennas and twenty-seven 25-m antennas were used to increase the gain by 5. Another example of a real-life linear equation is estimating the dimensions of a set of four shelves whose width needs to be five times its height, given that the wood available for use is 72 feet.
It is more difficult to estimate variable costs, as they can change based on a number of factors. Exponential smoothing can generate a forecast based on as little as one historical data point. Goods with this property will be defined later in this class as inferior goods. In general, budget constraints can be written in the form above unless they have special conditions such as volume discounts, rebates, etc. However, there are also cases of boundary optima as in the last part of this question where the two are not the same.