Managerial Economics Applications Strategies And Tactics 13th Edition By McGuigan

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Sample Questions

Chapter 4—Estimating Demand

MULTIPLE CHOICE

1. Using a sample of 100 consumers, a double-log regression model was used to estimate demand for gasoline. Standard errors of the coefficients appear in the parentheses below the coefficients.

Ln Q = 2.45 -0.67 Ln P + . 45 Ln Y – .34 Ln P_cars

(.20) (.10) (.25)

Where Q is gallons demanded, P is price per gallon, Y is disposable income, and P_cars is a price index for cars. Based on this information, which is NOT correct?

1. Gasoline is inelastic.

2. Gasoline is a normal good.

3. Cars and gasoline appear to be mild complements.

4. The coefficient on the price of cars (P_cars) is insignificant.

5. All of the coefficients are insignificant.

ANS: E PTS: 1

2. In a cross section regression of 48 states, the following linear demand for per-capita cans of soda was found: Cans = 159.17 – 102.56 Price + 1.00 Income + 3.94Temp

	Coefficients	Standard Error	t Stat
Intercept	159.17	94.16	1.69
Price	-102.56	33.25	-3.08
Income	1.00	1.77	0.57
Temperature	3.94	0.82	4.83

R-Sq = 54.1% R-Sq(adj) = 51.0%

From the linear regression results in the cans case above, we know that:

1. Price is insignificant

2. Income is significant

3. Temp is significant

4. As price rises for soda, people tend to drink less of it

5. All of the coefficients are significant

ANS: D PTS: 1

3. A study of expenditures on food in cities resulting in the following equation:

Log E = 0.693 Log Y + 0.224 Log N

where E is Food Expenditures; Y is total expenditures on goods and services; and N is the size of the family. This evidence implies:

1. that as total expenditures on goods and services rises, food expenditures falls.

2. that a one-percent increase in family size increases food expenditures .693%.

3. that a one-percent increase in family size increases food expenditures .224%.

4. that a one-percent increase in total expenditures increases food expenditures 1%.

5. that as family size increases, food expenditures go down.

ANS: C PTS: 1

4. All of the following are reasons why an association relationship may not imply a causal relationship except:

a.	the association may be due to pure chance
b.	the association may be the result of the influence of a third common factor
c.	both variables may be the cause and the effect at the same time
d.	the association may be hypothetical
e.	both c and d

ANS: D PTS: 1

5. In regression analysis, the existence of a significant pattern in successive values of the error term constitutes:

a.	heteroscedasticity
b.	autocorrelation
c.	multicollinearity
d.	nonlinearities
e.	a simultaneous equation relationship

ANS: B PTS: 1

6. In regression analysis, the existence of a high degree of intercorrelation among some or all of the explanatory variables in the regression equation constitutes:

a.	autocorrelation
b.	a simultaneous equation relationship
c.	nonlinearities
d.	heteroscedasticity
e.	multicollinearity

ANS: E PTS: 1

7. When using a multiplicative power function (Y = a X₁^b1 X₂^b2 X₃^b3) to represent an economic relationship, estimates of the parameters (a, and the b’s) using linear regression analysis can be obtained by first applying a ____ transformation to convert the function to a linear relationship.

a.	semilogarithmic
b.	double-logarithmic
c.	reciprocal
d.	polynomial
e.	cubic

ANS: B PTS: 1

8. The correlation coefficient ranges in value between 0.0 and 1.0.

a.	true
b.	false

ANS: B PTS: 1

9. The coefficient of determination ranges in value between 0.0 and 1.0.

a.	true
b.	false

ANS: A PTS: 1

10. The coefficient of determination measures the proportion of the variation in the independent variable that is “explained” by the regression line.

a.	true
b.	false

ANS: B PTS: 1

11. The presence of association between two variables does not necessarily imply causation for the following reason(s):

a.	the association between two variables may result simply from pure chance
b.	the association between two variables may be the result of the influence of a third common factor
c.	both variables may be the cause and the effect at the same time
d.	a and b
e.	a, b, and c

ANS: E PTS: 1

12. The estimated slope coefficient (b) of the regression equation (Ln Y = a + b Ln X) measures the ____ change in Y for a one ____ change in X.

a.	percentage, unit
b.	percentage, percent
c.	unit, unit
d.	unit, percent
e.	none of the above

ANS: B PTS: 1

13. The standard deviation of the error terms in an estimated regression equation is known as:

a.	coefficient of determination
b.	correlation coefficient
c.	Durbin-Watson statistic
d.	standard error of the estimate
e.	none of the above

ANS: D PTS: 1

14. In testing whether each individual independent variables (Xs) in a multiple regression equation is statistically significant in explaining the dependent variable (Y), one uses the:

a.	F-test
b.	Durbin-Watson test
c.	t-test
d.	z-test
e.	none of the above

ANS: C PTS: 1

15. One commonly used test in checking for the presence of autocorrelation when working with time series data is the ____.

a.	F-test
b.	Durbin-Watson test
c.	t-test
d.	z-test
e.	none of the above

ANS: B PTS: 1

16. The method which can give some information in estimating demand of a product that hasn’t yet come to market is:

a.	the consumer survey
b.	market experimentation
c.	a statistical demand analysis
d.	plotting the data
e.	the barometric method

ANS: A PTS: 1

17. Demand functions in the multiplicative form are most common for all of the following reasons except:

a.	elasticities are constant over a range of data
b.	ease of estimation of elasticities
c.	exponents of parameters are the elasticities of those variables
d.	marginal impact of a unit change in an individual variable is constant
e.	c and d

ANS: D PTS: 1

18. The Identification Problem in the development of a demand function is a result of:

a.	the variance of the demand elasticity
b.	the consistency of quantity demanded at any given point
c.	the negative slope of the demand function
d.	the simultaneous relationship between the demand and supply functions
e.	none of the above

ANS: D PTS: 1

19. Consider the following linear demand function where Q_D = quantity demanded, P = selling price, and Y = disposable income:

Q_D = -36 -2.1P + .24Y

The coefficient of P (i.e., -2.1) indicates that (all other things being held constant):

a.	for a one percent increase in price, quantity demanded would decline by 2.1 percent
b.	for a one unit increase in price, quantity demanded would decline by 2.1 units
c.	for a one percent increase in price, quantity demanded would decline by 2.1 units
d.	for a one unit increase in price, quantity demanded would decline by 2.1 percent
e.	none of the above

ANS: B PTS: 1

20. Consider the following multiplicative demand function where Q_D = quantity demanded, P = selling price, and Y = disposable income:

The coefficient of Y (i.e., .2) indicates that (all other things being held constant):

a.	for a one percent increase in disposable income, quantity demanded would increase by .2 percent
b.	for a one unit increase in disposable income, quantity demanded would increase by .2 units
c.	for a one percent increase in disposable income quantity demanded would increase by .2 units
d.	for a one unit increase in disposable income, quantity demanded would increase by .2 percent
e.	none of the above

ANS: A PTS: 1

21. One shortcoming of the use of ____ in demand analysis is that the participants are generally aware that their actions are being observed and hence they may seek to act in a manner somewhat different than normal.

a.	market experiments
b.	consumer clinics
c.	statistical (econometric) methods
d.	a and b
e.	none of the above

ANS: B PTS: 1

22. The constant or intercept term in a statistical demand study represents the quantity demanded when all independent variables are equal to:

a.	1.0
b.	their minimum values
c.	their average values
d.	0.0
e.	none of the above

ANS: D PTS: 1

23. Novo Nordisk A/S, a Danish firm, sells insulin and other drugs worldwide. Activella, an estrogen and progestin hormone replacement therapy sold by Novo-Nordisk, is examined using 33 quarters of data

Y = -204 + . 34X₁ – .17X₂

(17.0) (-1.71)

Where Y is quarterly sales of Activella, X₁ is the Novo’s advertising of the hormone therapy, and X₂ is advertising of a similar product by Eli Lilly and Company, Novo-Nordisk’s chief competitor. The parentheses contain t-values. Addition information is: Durbin-Watson = 1.9 and R²= .89.

Using the data for Novo-Nordisk, which is correct?

1. Both X₁ and X₂are statistically significant.

2. Neither X₁ nor X₂are statistically significant.

3. X₁ is statistically significant but X₂is not statistically significant.

4. X₁ is not statistically significant but X₂is statistically significant.

5. The Durbin-Watson statistic shows significant problems with autocorrelation

ANS: A PTS: 1

24. In which of the following econometric problems do we find Durbin-Watson statistic being far away from 2.0?

25. the identification problem

26. autocorrelation

27. multicollinearity

28. heteroscedasticity

29. agency problems

ANS: B PTS: 1

25. When there is multicollinearity in an estimated regression equation,

26. the coefficients are likely to be small.

27. the t‑statistics are likely to be small even though the R² is large.

28. the coefficient of determination is likely to be small.

29. the problem of omitted variables is likely.

30. the error terms will tend to have a cyclical pattern.

26. When two or more “independent” variables are highly correlated, then we have:

27. the identification problem

28. multicollinearity

29. autocorrelation

30. heteroscedasticity

31. complementary products

ANS: B PTS: 1

27. Which is NOT true about the coefficient of determination?

28. As you add more variables, the R-square generally rises.

29. As you add more variables, the adjusted R-square can fall.

30. If the R-square is above 50%, the regression is considered significant.

31. The R-square gives the percent of the variation in the dependent variable that is explained by the independent variables.

32. The higher is the R-square, the better is the fit.

ANS: C PTS: 1

28. Even though insignificant explanatory variables can raise the adjusted R² of a demand function, one should not interpret their effects on the regression when

29. testing marketing hypotheses about the determinants of demand

30. analyzing inventory relative to capacity requirements

31. forecasting unit sales for operations planning

32. sales revenue reaches its peak

33. planning for capital budgets

ANS: A PTS: 1

PROBLEMS

1. Phoenix Lumber Company uses the number of construction permits issued to help estimate demand (sales). The firm collected the following data on annual sales and number of construction permits issued in its market area:

	No. of Construction	Sales
Year	Permits Issued (000)	(1,000,000)

2003	6.50	10.30
2004	6.20	10.10
2005	6.60	10.50
2006	7.30	10.80
2007	7.80	11.20
2008	8.20	11.40
2009	8.30	11.30

(a)	Which variable is the dependent variable and which is the independent variable?
(b)	Determine the estimated regression line.
(c)	Test the hypothesis (at the .05 significance level) that there is no relationship between the variables.
(d)	Calculate the coefficient of determination. Give an economic interpretation to the value obtained.
(e)	Perform an analysis of variance on the regression including an F-test (at the .05 significance level) of the overall significance of the results.
(f)	Suppose that 8,000 construction permits are expected to be issued in 2010. What would be the point estimate of Phoenix Lumber Company’s sales for 2010?

ANS:

(a)	Dependent variable (Y) – Sales
	Independent variable (X) – No. of construction permits issued

(b)	Obs.
	(i)	Year	X_i	Y_i	X_iY_i	X_i²	Y_i²

	1	2003	6.50	10.30	66.95	42.25	106.09
	2	2004	6.20	10.10	62.62	38.44	102.01
	3	2005	6.60	10.50	69.30	43.56	110.25
	4	2006	7.30	10.80	78.84	53.29	116.64
	5	2007	7.80	11.20	87.36	60.84	125.44
	6	2008	8.20	11.40	93.48	67.24	129.96
	7	2009	8.30	11.30	93.79	68.89	127.69
			50.90	75.60	552.34	374.51	818.08
			SX_i	SY_i	SX_iY_i	SX_i²	SY_i²


	Alternatively, this project can be done using regression software or Excel.
(c)

From the t-distribution, the t_.025 value with 7-2 degrees of freedom is 2.571. Since the calculated t-value (14.726) is greater than the value from the table, we reject the hypothesis that there is no relationship between the variables.

(d)					Explained	Unexplained	Total
					SS	SS	SS

	i	X_i	Y_i	Y_i = 6.4648 + .5962X_i

	1	6.50	10.30	10.34010	.21151	.00161	.25000
	2	6.20	10.10	10.16124	.40801	.00375	.49000
	3	6.60	10.50	10.39972	.16022	.01006	.09000
	4	7.30	10.80	10.81706	.00029	.00029	.00000
	5	7.80	11.20	11.11516	.09933	.00720	.16000
	6	8.20	11.40	11.35364	.30652	.00215	.36000
	7	8.30	11.30	11.41326	.37609	.01283	.25000
					1.56197	.03789	1.60000

The regression equation “explains” 97.6% of the variation in the company’s sales.

(e)	Source of	Sum of	Degrees of
	Variation	Squares	Freedom	Mean Squares
	Regression	1.56197	1	1.56197
	Residual	.03789	5	.007578
	Total	1.60000*	6

	*Difference is due to round-off error

The value of F_{(.05; 1,5)} from the F-distribution is 6.61. Since the calculated F is greater than the value from the table, we reject the null hypothesis that there is no relationship between the company’s sales and the number of construction permits issues.

(f)

Estimated sales for Phoenix Lumber Company in 2010 would be $11.234 million.

PTS: 1 NOTE: This problem requires the use of statistical tables.

2. Lenny’s, a national restaurant chain, conducted a study of the factors affecting demand (sales). The following variables were defined and measured for a random sample of 30 of its restaurants:

Y	= Annual restaurant sales ($000)
X₁	= Disposable personal income (per capita) of residents within 5 mile radius
X₂	= License to sell beer/wine (0 = No, 1 = Yes)
X₃	= Location (within one-half mile of interstate highway–0 = No, 1 = Yes)
X₄	= Population (within 5 mile radius)
X₅	= Number of competing restaurants within 2 mile radius

The data were entered into a computerized regression program and the following results were obtained:

MULTIPLE R	.889
R-SQUARE	.79
STD. ERROR OF EST.	.40

ANALYSIS OF VARIANCE

	DF	Sum Squares	Mean Sqr.	F-Stat
Regression	5	326.13	65.226	18.17
Error	24	86.17	3.590
Total	29	412.30

Variable	Coefficient	Std. Error	T-Value

Constant	.363	.196	1.852
X-1	.00275	.00104	2.644
X-2	76.65	93.70	.818
X-3	164.3	235.4	.698
X-4	.00331	.00126	2.627
X-5	46.2	12.1	-3.818

Questions:

(a)	Give the regression equation for predicting restaurant sales.
(b)	Give an interpretation of each of the estimated regression coefficients.
(c)	Which of the independent variables (if any) are statistically significant at the .05 level in “explaining” restaurant sales?
(d)	What proportion of the variation in restaurant sales is “explained” by the regression equation?
(e)	Perform an F-test (at the .05 significance level) of the overall explanatory power of the regression model.

ANS:

(a)	Y = .363 + .00275X₁ + 76.65X₂ + 164.3X₃ + .00331X₄ – 46.2X₅

(b)	a = .363	Value of dependent variable (Y) when all independent variables (X’s) are equal to zero.
	b₁ = .00275	For a one dollar increase in per capita disposable income, expected restaurant sales will increase by .00275(´ $1000) = $2.7
	b₂ = 76.65	Expected annual restaurant sales are 76.65(´ $1000) = $76,650 higher for a restaurant with a license to sell beer/wine than for one without such a license.
	b₃ = 164.3	Expected annual restaurant sales are 164.3(´ $1000) = $164,300 higher for a restaurant located within one-half mile of an interstate highway.
	b₄ = .00331	For a one person increase in population, expected restaurant sales will increase by .00331(´ $1000) = $3.31.
	b₅ = -46.2	For a one unit increase in the number of restaurants within a 2-mile radius, expected annual restaurant sales decrease by 46.2(´ $1000) = $46,200.

(c)	H₀: b_i = 0
	H₁: b_i ¹ 0
	Reject H₀ if t > t_{.025, 24} = 2.064 or t < -2.064.

	The t-values of X₁ and X₄ are greater than +2.064 (and the t-value of X₅ is less than -2.064). Therefore X₁, X₄, and X₅ are statistically significant at the .05 level in “explaining” restaurant sales.

(d)	According to the R-SQUARE statistic, 79 percent of the variation in restaurant sales is “explained” by the regression equation.

(e)	H₀: All b_i = 0 (no relationship)
	H₁: At least one b_i ¹ 0
	Reject H₀ if F > F_{.05, 5, 24} = 2.62

	The F-STAT is equal to 18.18, which exceeds 2.62. Therefore, one rejects the null hypothesis (at the .05 significance level) and concludes that the five independent variables “explain” a significant proportion of the variation in restaurant sales.

PTS: 1 NOTE: This problem requires the use of statistical tables.

3. The following demand function has been estimated for Fantasy pinball machines:

Q_D = 3,500 – 40P + 17.5P_x + 670U + .0090A + 6,500N

where	P = monthly rental price of Fantasy pinball machines
	P_x = monthly rental price of Old Chicago pinball machines (their largest competitor)
	U = current unemployment rate in the 10 largest metropolitan areas
	A = advertising expenditures for Fantasy pinball machines
	N = fraction of the U.S. population between ages 10 and 30

(a)	What is the point price elasticity of demand for Fantasy pinball machines when P = $150, P_x = $100, U = .12, A = $200,000 and N = .35?
(b)	What is the point cross elasticity of demand with respect to Old Chicago pinball machines for the values of the independent variables given in part (a)?

ANS:

(a)

(b)

PTS: 1

4. Given the following demand function:

Q = 2.0 P^–1.33 Y^2.0 A^.50

where	Q = quantity demanded (thousands of units)
	P = price ($/unit)
	Y = disposable income per capita ($ thousands)
	A = advertising expenditures ($ thousands)

determine the following when P = $2/unit, Y = $8 (i.e., $8000), and A = $25 (i.e., $25,000)

(a)	Price elasticity of demand
(b)	The approximate percentage increase in demand if disposable income percentage increases by 3%.
(c)	The approximate percentage increase in demand if advertising expenditures are increased by 5 percent.

ANS:

(a)	E_D = -1.33 (independent of other variables)

(b)	Since E_Y = -2.0, a 3% increase in disposable income would yield an approximate


	or a 6% increase in demand.

(c)	Since E_A = 0.50, a 5% increase in advertising expenditures would yield an approximate



	or a 2.5% increase in demand

PTS: 1

Chapter 7—Production Economics

MULTIPLE CHOICE

1. What’s true about both the short-run and long-run in terms of production and cost analysis?

2. In the short-run, one or more of the resources are fixed

3. In the long-run, all the factors are variable

4. The time horizon determines whether or not an input variable is fixed or not

5. The law of diminishing returns is based in part on some factors of production being fixed, as they are in the short run.

6. All of the above

ANS: E PTS: 1

2. The marginal product is defined as:

a. The ratio of total output to the amount of the variable input used in producing the output

b. The incremental change in total output that can be produced by the use of one more unit of the variable input in the production process

c. The percentage change in output resulting from a given percentage change in the amount

d. The amount of fixed cost involved.

e. None of the above

ANS: B PTS: 1

3. Fill in the missing data to solve this problem.

Variable Total Average Marginal

Input Product Product Product

4 ? 70 —-

5 ? ? 40

6 350 ? ?

What is the total product for 5 units of input, and what is the marginal product for 6 units of input?

1. 320 and 30

2. 350 and 20

3. 360 and 15

4. 400 and 10

5. 430 and 8

ANS: A PTS: 1

4. The following is a Cobb-Douglas production function: Q = 1.75K⁵∙L^0.5. What is correct here?

a. A one-percent change in L will cause Q to change by one percent

b. A one-percent change in K will cause Q to change by two percent

c. This production function displays increasing returns to scale

d. This production function displays constant returns to scale

e. This production function displays decreasing returns to scale

ANS: D PTS: 1

5. Suppose you have a Cobb-Douglas function with a capital elasticity of output (α) of 0.28 and a labor elasticity of output (β) of 0.84. What statement is correct?

a. There are increasing returns to scale

b. If the amount of labor input (L) is increased by 1%, the output will increase by 0.84%

c. If the amount of capital input (K) is decreased by 1%, the output will decrease by 0.28%

d. The sum of the exponents in the Cobb-Douglas function is 1.12.

e. All of the above

ANS: E PTS: 1

6. The Cobb-Douglas production function is: Q = 1.4*L⁶*K^0.5. What would be the percentage change in output (%∆Q) if labor grows by 3.0% and capital is cut by 5.0%?

[Hint: %∆Q = (E_L * %∆L) + (E_K * %∆K)]

3. %∆Q = + 3.0%

4. %∆Q = + 5.0%

5. %∆Q = – 0.70%

6. %∆Q = – 2.50%

7. %∆Q = – 5.0%

ANS: C PTS: 1

7. If the marginal product of labor is 100 and the price of labor is 10, while the marginal product of capital is 200 and the price of capital is $30, then what should the firm?

a. The firm should use relatively more capital

b. The firm should use relatively more labor

c. The firm should not make any changes – they are currently efficient

d. Using the Equimarginal Criterion, we can’t determine the firm’s efficiency level

e. Both c and d

ANS: B PTS: 1

8. The marginal rate of technical substitution may be defined as all of the following except:

a.	the rate at which one input may be substituted for another input in the production process, while total output remains constant
b.	equal to the negative slope of the isoquant at any point on the isoquant
c.	the rate at which all combinations of inputs have equal total costs
d.	equal to the ratio of the marginal products of X and Y
e.	b and c

ANS: C PTS: 1

9. The law of diminishing marginal returns:

a.	states that each and every increase in the amount of the variable factor employed in the production process will yield diminishing marginal returns
b.	is a mathematical theorem that can be logically proved or disproved
c.	is the rate at which one input may be substituted for another input in the production process
d.	none of the above

ANS: D PTS: 1

10. The combinations of inputs costing a constant C dollars is called:

a.	an isocost line
b.	an isoquant curve
c.	the MRTS
d.	an isorevenue line
e.	none of the above

ANS: A PTS: 1

11. In a relationship among total, average and marginal products, where TP is maximized:

a.	AP is maximized
b.	AP is equal to zero
c.	MP is maximized
d.	MP is equal to zero
e.	none of the above

ANS: D PTS: 1

12. Holding the total output constant, the rate at which one input X may be substituted for another input Y in a production process is:

a.	the slope of the isoquant curve
b.	the marginal rate of technical substitution (MRTS)
c.	equal to MP_x/MP_y
d.	all of the above
e.	none of the above

ANS: D PTS: 1

13. Which of the following is never negative?

a.	marginal product
b.	average product
c.	production elasticity
d.	marginal rate of technical substitution
e.	slope of the isocost lines

ANS: B PTS: 1

14. Concerning the maximization of output subject to a cost constraint, which of the following statements (if any) are true?

a.	At the optimal input combination, the slope of the isoquant must equal the slope of the isocost line.
b.	The optimal solution occurs at the boundary of the feasible region of input combinations.
c.	The optimal solution occurs at the point where the isoquant is tangent to the isocost lines.
d.	all of the above
e.	none of the above

ANS: D PTS: 1

15. In a production process, an excessive amount of the variable input relative to the fixed input is being used to produce the desired output. This statement is true for:

a.	stage II
b.	stages I and II
c.	when Ep = 1
d.	stage III
e.	none of the above

ANS: D PTS: 1

16. Marginal revenue product is:

a.	defined as the amount that an additional unit of the variable input adds to the total revenue
b.	equal to the marginal factor cost of the variable factor times the marginal revenue resulting from the increase in output obtained
c.	equal to the marginal product of the variable factor times the marginal product resulting from the increase in output obtained
d.	a and b
e.	a and c

ANS: A PTS: 1

17. The isoquants for inputs that are perfect substitutes for one another consist of a series of:

a.	right angles
b.	parallel lines
c.	concentric circles
d.	right triangles
e.	none of the above

ANS: B PTS: 1

18. In production and cost analysis, the short run is the period of time in which one (or more) of the resources employed in the production process is fixed or incapable of being varied.

a.	true
b.	false

ANS: A PTS: 1

19. Marginal revenue product is defined as the amount that an additional unit of the variable input adds to ____.

a.	marginal revenue
b.	total output
c.	total revenue
d.	marginal product
e.	none of the above

ANS: C PTS: 1

20. Marginal factor cost is defined as the amount that an additional unit of the variable input adds to ____.

a.	marginal cost
b.	variable cost
c.	marginal rate of technical substitution
d.	total cost
e.	none of the above

ANS: D PTS: 1

21. The isoquants for inputs that are perfect complements for one another consist of a series of:

a.	right angles
b.	parallel lines
c.	concentric circles
d.	right triangles
e.	none of the above

ANS: A PTS: 1

22. Given a Cobb-Douglas production function estimate of Q = 1.19L^.72K^.18 for a given industry, this industry would have:

a.	increasing returns to scale
b.	constant returns to scale
c.	decreasing returns to scale
d.	negative returns to scale
e.	none of the above

ANS: C PTS: 1

23. The primary purpose of the Cobb-Douglas power function is to:

a.	allow one to make estimates of cost-output relationships
b.	allow one to make predictions about a resulting increase in output for a given increase in the inputs
c.	aid one in gaining accurate empirical values for economic variables
d.	calculate a short-run linear total cost function
e.	a and b

ANS: B PTS: 1

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