This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
ScanSolve AI Answer
Step 1: Divide the data into two equal halves. There are 12 data points (months from January to December 1979). First half (Months 1-6): 280, 300, 280, 280, 270, 240 Second half (Months 7-12): 230, 230, 220, 200, 210, 200 Step 2: Calculate the semi-average for each half. First semi-average (S_1): S_1 = (280 + 300 + 280 + 280 + 270 + 240)/(6) = (1650)/(6) = 275 This average corresponds to the mid-point of the first half. The months are 1, 2, 3, 4, 5, 6. The mid-point is between month 3 and month 4, which is T_1 = 3.5. Second semi-average (S_2): S_2 = (230 + 230 + 220 + 200 + 210 + 200)/(6) = (1290)/(6) = 215 This average corresponds to the mid-point of the second half. The months are 7, 8, 9, 10, 11, 12. The mid-point is between month 9 and month 10, which is T_2 = 9.5. Step 3: Determine the trend line equation Y_t = a + bT. We have two points (T_1, S_1) = (3.5, 275) and (T_2, S_2) = (9.5, 215). Calculate the slope (b): b = (S_2 - S_1)/(T_2 - T_1) = (215 - 275)/(9.5 - 3.5) = (-60)/(6) = -10 Calculate the y-intercept (a) using one of the points, for example (3.5, 275): S_1 = a + bT_1 275 = a + (-10)(3.5) 275 = a - 35 a = 275 + 35 a = 310 Step 4: Write the trend line equation. The trend line equation is Y_t = a + bT. Y_t = 310 - 10T where Y_t is the sales in tonnes and T is the month number (e.g., T=1 for January, T=2 for February, etc.). The trend line equation is Y_t = 310 - 10T. That's 2 down. 3 left today — send the next one.