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sir please help me for following question

1. "The opportunity cost of anything is the return that can be had from the next best 20 alternative use". Elucidate the statement with reference to the opportunity cost principle applied in agricultural sector.

2. The demand function is written as Qd= F (Po, Pc, Ps, Yd, T, A, CR, R, E, N, 0) Describe 20 each of this variables separately giving examples.

3. What do you understand by 'Price discrimination' and the various types of price 20 discrimination ? I-low is the optimal quantity to be supplied in different markets determined ? Elucidate your answer with suitable examples.

4. Define elasticity of demand. How are the price, income, cross elasticities measured ?"

5. time series analysis of demand forecasting?

5. time series analysis of demand forecasting?

TIME SERIES METHODS OF FORECASTING.

Before discussing time series methods, it is helpful to understand the behavior of time series in general terms. Time series are comprised of four separate components: trend component, cyclical component, seasonal component, and irregular component. These four components are viewed as providing specific values for the time series when combined.

In a time series, measurements are taken at successive points or over successive periods. The measurements may be taken every hour, day, week, month, or year, or at any other regular (or irregular) interval. While most time series data generally display some random fluctuations, the time series may still show gradual shifts to relatively higher or lower values over an extended period. The gradual shifting of the time series is often referred to by professional forecasters as the trend in the time series. A trend emerges due to one or more long-term factors, such as changes in population size, changes in the demographic characteristics of population, and changes in tastes and preferences of consumers. For example, manufacturers of automobiles in the United States may see that there are substantial variations in automobile sales from one month to the next. But, in reviewing auto sales over the past 15 to 20 years, the automobile manufacturers may discover a gradual increase in annual sales volume. In this case, the trend for auto sales is increasing over time. In another example, the trend may be decreasing over time. Professional forecasters often describe an increasing trend by an upward sloping straight line and a decreasing trend by a downward sloping straight line. Using a straight line to represent a trend, however, is a mere simplification—in many situations, nonlinear trends may more accurately represent the true trend in the time series.

Although a time series may often exhibit a trend over a long period, it may also display alternating sequences of points that lie above and below the trend line. Any recurring sequence of points above and below the trend line that last more than a year is considered to constitute the cyclical component of the time series—that is, these observations in the time series deviate from the trend due to cyclical fluctuations (fluctuations that repeat at intervals of more than one year). The time series of the aggregate output in the economy (called the real gross domestic product) provides a good example of a time series that displays cyclical behavior. While the trend line for gross domestic product (GDP) is upward sloping, the output growth displays a cyclical behavior around the trend line. This cyclical behavior of GDP has been dubbed business cycles by economists.

The seasonal component is similar to the cyclical component in that they both refer to some regular fluctuations in a time series. There is one key difference, however. While cyclical components of a time series are identified by analyzing multiyear movements in historical data, seasonal components capture the regular pattern of variability in the time series within one-year periods. Many economic variables display seasonal patterns. For example, manufacturers of swimming pools experience low sales in fall and winter months, but they witness peak sales of swimming pools during spring and summer months. Manufacturers of snow removal equipment, on the other hand, experience the exactly opposite yearly sales pattern. The component of the time series that captures the variability in the data due to seasonal fluctuations is called the seasonal component.

The irregular component of the time series represents the residual left in an observation of the time series once the effects due to trend, cyclical, and seasonal components are extracted. Trend, cyclical, and seasonal components are considered to account for systematic variations in the time series. 'h e irregular component thus accounts for the random variability in the time series. The random variations in the time series are, in turn, caused by short-term, unanticipated and nonrecurring factors that affect the time series. The irregular component of the time series, by nature, cannot be predicted in advance.

TIME SERIES FORECASTING USING SMOOTHING METHODS.

Smoothing methods are appropriate when a time series displays no significant effects of trend, cyclical, or seasonal components (often called a stable time series). In such a case, the goal is to smooth out the irregular component of the time series by using an averaging process. Once the time series is smoothed, it is used to generate forecasts.

The moving averages method is probably the most widely used smoothing technique. In order to smooth the time series, this method uses the average of a number of adjoining data points or periods. This averaging process uses overlapping observations to generate averages. Suppose a forecaster wants to generate three-period moving averages. The forecaster would take the first three observations of the time series and calculate the average. Then, the forecaster would drop the first observation and calculate the average of the next three observations. This process would continue until three-period averages are calculated based on the data available from the entire time series. The term "moving" refers to the way averages are calculated—the forecaster moves up or down the time series to pick observations to calculate an average of a fixed number of observations. In the three-period example, the moving averages method would use the average of the most recent three observations of data in the time series as the forecast for the next period. This forecasted value for the next period, in conjunction with the last two observations of the historical time series, would yield an average that can be used as the forecast for the second period in the future.

The calculation of a three-period moving average can be illustrated as follows. Suppose a forecaster wants to forecast the sales volume for American-made automobiles in the United States for the next year. The sales of American-made cars in the United States during the previous three years were: 1.3 million, 900,000, and 1.1 million (the most recent observation is reported first). The three-period moving average in this case is 1.1 million cars (that is: [(1.3 + 0.90 + 1.1)/3 = 1.1]). Based on the three-period moving averages, the forecast may predict that 1.1 million American-made cars are most likely to be sold in the United States the next year.

In calculating moving averages to generate forecasts, the forecaster may experiment with different-length moving averages. The forecaster will choose the length that yields the highest accuracy for the forecasts generated.

" It is important that forecasts generated not be too far from the actual future outcomes. In order to examine the accuracy of forecasts generated, forecasters generally devise a measure of the forecasting error (that is, the difference between the forecasted value for a period and the associated actual value of the variable of interest). Suppose retail sales volume for American-made automobiles in the United States is forecast to be 1.1 million cars for a given year, but only I million cars are actually sold that year. The forecast error in this case is equal 100,000 cars. In other words, the forecaster overestimated the sales volume for the year by 100,000. Of course, forecast errors will sometimes be positive, and at other times be negative. Thus, taking a simple average of forecast errors over time will not capture the true magnitude of forecast errors; large positive errors may simply cancel out large negative errors, giving a misleading impression about the accuracy of forecasts generated. As a result, forecasters commonly use the mean squares error to measure the forecast error. The mean squares error, or the MSE, is the average of the sum of squared forecasting errors. This measure, by taking the squares of forecasting errors, eliminates the chance of negative and positive errors canceling out.

In selecting the length of the moving averages, a forecaster can employ the MSE measure to determine the number of values to be included in calculating the moving averages. The forecaster experiments with different lengths to generate moving averages and then calculates forecast errors (and the associated mean squares errors) for each length used in calculating moving averages. Then, the forecaster can pick the length that minimizes the mean squared error of forecasts generated.

Weighted moving averages are a variant of moving averages. In the moving averages method, each observation of data receives the same weight. In the weighted moving averages method, different weights are assigned to the observations on data that are used in calculating the moving averages. Suppose, once again, that a forecaster wants to generate three-period moving averages. Under the weighted moving averages method, the three data points would receive different weights before the average is calculated. Generally, the most recent observation receives the maximum weight, with the weight assigned decreasing for older data values.

The calculation of a three-period weighted moving average can be illustrated as follows. Suppose, once again, that a forecaster wants to forecast the sales volume for American-made automobiles in the United States for the next year. The sales of American-made cars for the United States during the previous three years were: 1.3 million, 900,000, and 1.1 million (the most recent observation is reported first). One estimate of the weighted three-period moving average in this example can be equal to 1.133 million cars (that is, [ 1(3/6) x (1.3) + (2/6) x (0.90) + (1/6) x (1.1)}/ 3 = 1.133 ]). Based on the three-period weighted moving averages, the forecast may predict that 1.133 million American-made cars are most likely to be sold in the United States in the next year. The accuracy of weighted moving averages forecasts are determined in a manner similar to that for simple moving averages.

Exponential smoothing is somewhat more difficult mathematically. In essence, however, exponential smoothing also uses the weighted average concept—in the form of the weighted average of all past observations, as contained in the relevant time series—to generate forecasts for the next period. The term "exponential smoothing" comes from the fact that this method employs a weighting scheme for the historical values of data that is exponential in nature. In ordinary terms, an exponential weighting scheme assigns the maximum weight to the most recent observation and the weights decline in a systematic manner as older and older observations are included. The accuracies of forecasts using exponential smoothing are determined in a manner similar to that for the moving averages method.

TIME SERIES FORECASTING USING TREND PROJECTION.

This method uses the underlying long-term trend of a time series of data to forecast its future values. Suppose a forecaster has data on sales of American-made automobiles in the United States for the last 25 years. The time series data on U.S. auto sales can be plotted and examined visually. Most likely, the auto sales time series would display a gradual growth in the sales volume, despite the "up" and "down" movements from year to year. The trend may be linear (approximated by a straight line) or nonlinear (approximated by a curve or a nonlinear line). Most often, forecasters assume a linear trend—of course, if a linear trend is assumed when, in fact, a nonlinear trend is present, this misrepresentation can lead to grossly inaccurate forecasts. Assume that the time series on American-made auto sales is actually linear and thus it can be represented by a straight line. Mathematical techniques are used to find the straight line that most accurately represents the time series on auto sales. This line relates sales to different points over time. If we further assume that the past trend will continue in the future, future values of the time series (forecasts) can be inferred from the straight line based on the past data. One should remember that the forecasts based on this method should also be judged on the basis of a measure of forecast errors. One can continue to assume that the forecaster uses the mean squares error discussed earlier.

TIME SERIES FORECASTING USING TREND AND SEASONAL COMPONENTS.

This method is a variant of the trend projection method, making use of the seasonal component of a time series in addition to the trend component. This method removes the seasonal effect or the seasonal component from the time series. This step is often referred to as de-seasonalizing the time series.

Once a time series has been de-seasonalized it will have only a trend component. The trend projection method can then be employed to identify a straight line trend that represents the time series data well. Then, using this trend line, forecasts for future periods are generated. The final step under this method is to reincorporate the seasonal component of the time series (using what is known as the seasonal index) to adjust the forecasts based on trend alone. In this manner, the forecasts generated are composed of both the trend and seasonal components. One will normally expect these forecasts to be more accurate than those that are based purely on the trend projection.

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