1. A consulting firm estimated the market demand and supply functions for coal in 2014 and obtained the following results:
Demand: Q = 590 -5p + 0.01M + 20PR
Supply: Q + 300 + 5P - 18P1
Where Q = quantity of coal (millions of tons), P = real price of coal ($ / ton), M = income per capital, PR + real price of oil ($/barrel), and P1 Coal Miners wage rate ($ / hour). The forecasted values for 2014 are 2014 are M = $25,000, PR = $15, and P1 = $20.
a. What is the forecasted price of coal for 2014?
b. What are the forecasted sales of coal in 2014?
c. The forecast of coal miners wage rate for 2014 depends on the new union contract that will be negotiated in 2014. The union manages to will additional concessions that increase the wage rate (P1) to $25, while the forecasted values of M and PR are unchanged (M= $25,000 and PR =$15). What will be the new price and output forecasts for 2014?
2. A forecaster used the regression equation:
Q1 a + bt + c1D1 + c2D2 + c3D3
And quarterly sales data for 1998I - 2013IV (t = 1,....., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2 and D3 are dummy variables for quarters I, II, and III.
DEPENDENT P-VALUE
VARIABLE QT R-SQUARE F-RATIO ON F
OBSERVATIONS 64 0.8768 107.982 0.0001
VARIABLES PARAMETER STANDARD
ESTIMATE ERROR T-RATIO P-VALUE
INTERCEPT 30.0 12.8 2.34 0.0224
T 1.5 0.70 2.14 0.0362
D1 10.0 3.0 333 0.0517
D2 25.0 7.2 3.47 0.0010
D3 40.0 15.8 2.5 0.0140
a. At the 5 percent level of significance, is there a statistically significant trend in sales? Why?
b. What is the estimated ANNUAL increase in sales?
c. What is the estimated intercept of the trend line in the second quarter
d. Calculate the predicted level of sales for each of the four quarters of 2014.
3. EconoLuv, an econometric consulting firm, estimated the world demand for oil using a linear specification, Q = a + bP + eM + dPR, where Q = millions of Barrels of oil, P = real price of oil, M = average real income per household in Industrialized nations, and PR = real price of coal. The consultants at EconoDat obtained these results:
DEPENDENT P-VALUE
VARIABLE Q R-SQUARE F-RATIO ON F
OBSERVATIONS 20 0.8499 30.210 0.0001
VARIABLES PARAMETER STANDARD
ESTIMATE ERROR T-RATIO P-VALUE
INTERCEPT -5740.00 1640.6 -3.50 0.0030
P -83.5 18.50 -4.51 0.0004
M 0.5698 0.19123 2.98 0.0088
PR 53.3 27.5 1.94 0.0700
Currently, P = $30, M = $20,000, PR = $40
a. What is the estimated quantity of oil demanded?
b. What is the estimated price elasticity of demand in the current situation
c. If the price of coal falls to $30, all else constant, what will happen to the estimated quantity of oil demanded?
d. If the price of oil decreases 5%, what will happen to the estimated quantity of oil demanded?
e. Calculate the estimated income elasticity.