Chapter 5

Question 3 Metropolitan Hospital has estimated its average monthly bed needs as N = 1,000 + 9X X = time period (months); January 2002 = 0 N = monthly bed needs Assume that no new hospital additions are expected in the area in the foreseeable future. The following monthly monthly seasonal adjustment factors have been estimated, using data from the past 5 years: ADJUSTMENT FACTOR MONTH X = time period (months) Jan + 5% 5 years X 5 = 60 Apr - 15% 60 + 3 = 63 Jul + 4% 63 + 3 = 66 Nov - 5% 66 + 4 = 70 De c - 25% 70 + 1 = 71 a) Forecast Metropolitan's bed demand for Jan, Apr, Jul, Nov and Dec 2007. Jan 2002 - Jan Jan 2007; x = (2007 - 2002) 2002) x 12 = 60 Jan 2007 2007 - Apr 2007; x = 60 + 3 = 63 Apr 2007 - Jul 2007; x = 63 + 3 = 66 Jul 2007 2007 - Nov 2007; x = 66 + 4 = 70 Nov 2007 2007 - Dec Dec 2007; 2007; x = 70 + 1 = 71 Jan-07 N= N= Fore Foreca cast st bed bed dem deman and d= Fore Foreca cast st bed bed d dem eman and d= Fore Foreca cast st bed bed dem deman and d=

1000 1000 + 9(60) 9(60) 1540 540 N x 1.05 1.05 1540 1540 x 1.0 1.05 5 1617 1617

Apr-07 N= N= Fore Foreca cast st bed bed dem deman and d= Fore Foreca cast st bed bed d dem eman and d= Fore Foreca cast st bed bed dema demand nd =

1000 1000 + 9(63) 9(63) 1567 567 N x 0.85 0.85 1567 1567 x 0.8 0.85 5 1331 1331.9 .95 5

Jul-07 N= N= Fore Foreca cast st bed bed dem deman and d= Fore Foreca cast st bed bed d dem eman and d= Fore Foreca cast st bed bed dema demand nd =

1000 1000 + 9(66) 9(66) 1594 594 N x 1.04 1.04 1594 1594 x 1.0 1.04 4 1657 1657.7 .76 6

Nov-07 N = 1000 1000 + 9(70) 9(70) N = 1630 630

Forecast bed demand = Forecast bed demand = Forecast bed demand =

N x 0.95 1630 x 0.95 1548.5

Dec-07 N= N= Forecast bed demand = Forecast bed demand = Forecast bed demand =

1000 + 9(71) 1639 N x 0.75 1639 x 0.75 1229.25

b) If the following actual and forecast values for June bed demands have been recorded, what seasonal adjustment factor would u recommend be used in making future June forecast? Year Forecast Actual Actual / Forecast 2007 1045 1096 1.048803828 2006 937 993 1.059765208 2005 829 897 1.082026538 2004 721 751 1.041608877 2003 613 628 1.024469821 2002 505 560 1.108910891 Sum 6.365585162 Min Seasonal adjustment factor = 6%

1.06093086

Question 4 Corporate profits (Pt - 1) for all firms in Indula were about $100 billion. GDP for the nation is composed of consumption C, investment I, and government spending G. It is anticipated that Indula's federal, state and local governments will spend in the range of $200 billion next year. On the basis of an analysis of recent economic activity in Indula, consumption expenditures are assumes to be $100 billion plus 80% of national income. National income is equal to GDP minus taxes T. Taxes are estimated to be at a rate of about 30% of  GDP. Finally corporate investment have historically equalled $30 billion plus 90% of last year's corporate profits (Pt - 1) a) Construct 5 equation econometric model of the state of Indula. There will be a consumption equation, an investment equation, a tax receipt equation, an equation representing the GDP identity, and a national income equation. (1) GDP = C + I + G (2) C = 100 + 0.8Y (3) Y = GDP - T Y = Income (4) T = 0.3GDP (5) I = 30 + 0.9(Pt - 1)

b) Assuming all random disturbance average to zero, solve the system of equations to arrive at next year's forecast values for C, I, T GDP and Y. (PT - 1) = $100 billion G = $200 billion I = 30 + 0.9(Pt - 1) I = 30 + 0.9(100) I= $ 120 billion C = 100 + 0.8Y 100 + 0.8(GDP - 0.3GDP) 100 + 0.56GDP GDP = 0.44 GDP = GDP = GDP =

100 + 0.56GDP + 120 + 200 420 420 / 0.44 $ 955 billion

C = 100 + 0.56(955) C= $ 635 billion T = 0.3(GDP) T = 0.3(955) T= $ 287 billion Y = GDP - T Y = 955 - 287

Y= $

668 billion

Question 7 Year 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Sales ($000) 121 130 145 160 155 179 215 208 235 262

t 0 1 2 3 4 5 6 7 8 9 10

a) Compute the quation of a trend line for these sales data to forecast sales for the next year. What does this equation forecast for sales in the year 2007? SUMMARY OUTPUT Regression Statistics

Multiple R R Square Adjusted R Square Standard Error Observations

0.97672616 0.95399399 0.94824324 10.7191418 10

ANOVA df

Regression Residual Total

SS

1 8 9

19060.8 919.2 19980

Coefficients Standard Error

Intercept t

112.6 15.2

MS

Sales = 112.6 + 15.2(10) Sales = 264.6 ($000)

Significance F  

19060.8 165.89034 114.9

1.24816E-06

t Stat

P-value

Lower 95%

9.842E-08 1.248E-06

98.07167483 127.12833 98.0716748 12.47859536 17.921405 12.4785954

6.300216446 17.8724 1.180138667 12.87984

Sales = 112.6 + 15.2 (t) 2007, t = 10

F

Upper 95% Lower 95.0% Upper 95.0%

127.128325 17.9214046

Question 9 Saving-Mart developed the following quaterly sales forecasting model: Yt = 8.25 + 0.125t - 2.75D1t + 0.25D2t + 3.5D3t Yt = predicted sales ($million) in quarter t 8.25 = quaterly sales ($million) when t = 0 t = time period (quarter) where the 4th quarter of 2002 = 0, 1st quarter of 2003 = 1, 2nd quarter of 2003 = 2. D1t = 1 for 1st quarter observations

D2t = 1 for 2nd quarter obse

0 otherwise

0 otherwise

D3t = 1 for 3rd quarter observations 0 otherwise Forecast Saving-Mart's sales of patio and lawn furniture for each quarter of 2010.

2002.4 2003.1 2003.2 2003.3 2003.4 . . . . . . 2010.1 2010.2 2010.3 2010.4

D1t

D2t

D3t

t

0 1 0 0 0 . . . . . . 1 0 0 0

0 0 1 0 0 . . . . . . 0 1 0 0

0 0 0 1 0 . . . . . . 0 0 1 0

0 1 2 3 4 . . . . . . 29 30 31 32

1st Quarter 2010 (2010.1)

Yt = 8.25 + 0.125t - 2.75D1t + 0.25D2t + 3.5D3t Yt = 8.25 + 0.125(29) - 2.75(1) + 0 + 0 Yt = 9.125 2nd Quarter 2010 (2010.2)

Yt = 8.25 + 0.125t - 2.75D1t + 0.25D2t + 3.5D3t Yt = 8.25 + 0.125(30) - 0 + 0.25(1) + 0 Yt = 12.25 3rd Quarter 2010 (2010.1)

Yt = 8.25 + 0.125t - 2.75D1t + 0.25D2t + 3.5D3t

Yt = 8.25 + 0.125(31) - 0 + 0 + 3.5(1) Yt = 15.625 1st Quarter 2010 (2010.1)

Yt = 8.25 + 0.125t - 2.75D1t + 0.25D2t + 3.5D3t Yt = 8.25 + 0.125(32) - 0 + 0 + 0 Yt = 12.25