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values for parameters obtained from regression

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Use the following to answer a-e. Please show all work in as much detail as possible. Assume Q is the quantity demanded for medical care services. The linear industry demand function takes the form

Q = a +bp +cM +dPr

where:
P = the price of the medical care
M = median household income
Pr = the price of a related good

dependent variable: Q R-square F-ratio P-value on F
0.8118 28.75 0.0001

Observations: 24

Variable PARAMETER ESTIMATE std error T-Ratio P-value

INTERCEPT 68.38 12.665 5.41 0.0001
P -6.5 3.15 -2.06 0.0492
M 0.13926 0.0131 10.63 0.0001
PR -10.77 2.45 -4.4 0.0002

a. Is the sign of ^b (hat over b) as would be predicted theoretically? Why/
b. What does the sign of ^c(hat over c) imply about the good?
c. what does the sign of ^d imply about the relation between the medical good and the related good R?
d. Are the parameter estimates ^a, ^b, ^c, and ^d statistically significant at the 5% level of significance?
e. Using the values P = 225, M= 24,000, and Pr =60, calculate the estimates of
(1) the price elasticity of demand (^Ed)
(2) the income elasticity of demand (^Ey)
(3) the cross-price elasticity (^Ec)

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Solution Preview

The equation given in the question is

Q = a +bp +cM +dPr

where

P = the price of the medical care
M = median household income
Pr = the price of a related good

The table provides various values for parameters obtained from regression. Before addressing those it will be a good idea to determine what signs to expect from each parameter above (b, c, d), and why should that parameter have that particular sign. To begin with consider b, the parameter with the variable p that is the price of medical care. One would expect the quantity demanded to fall as price of care goes up, that is as p rises Q should fall, and that is possible if b is less than zero, that is b is negative. M is the median household income, an indicator of wealth. The wealthier people get the more they can pay for medical care, and hence one would expect that the parameter with M, c should be positive. Finally, assuming that there is a related good d is the parameter associated with the price of the related good. One point to note here is that the related good may be a substitute (that is something that can be used instead of healthcare, and I cannot think of a substitute here!), or a complement (that is something that is ...

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Regression/sustainability/AVC/SMC

Please assist with all parts. Thank you!!!

Palm Products Company has collected data on its average variable costs of production for the past 12 months. The costs have been adjusted for inflation by deflating with an appropriate price index. The AVC and associated output data are presented below:

obs Q AVC obs Q AVC
1 22 $208 7 45 $172
2 31 202 8 45 158
3 31 206 9 45 173
4 25 214 10 62 170
5 41 174 11 62 152
6 41 203 12 70 175

a. Run the appropriate regression (below) to estimate the parameters for the empirical cost function:
AVC = a + bQ + cQ2

(Post your computer output here)

b. Using a 10 percent significance level test for the statistical significance of the parameters obtained in a, then discuss the suitability (considering their algebraic signs) of the parameter estimates.

c. Present (state) the estimated average variable cost, total variable cost, and short-run marginal cost functions.

d. (i) At what level of output does AVC reach its minimum value?
(ii) What is the minimum value of AVC at its minimum?

e. (i) Compute AVC and SMC when Palm Products produces 20 units of output:
(ii) Is AVC rising or falling when Palm produces 20 units? Explain.

f. At what level of output does SMC equal AVC? How did you get this answer?

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