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- May 23, 2018

MANAGERIAL ECONOMICS 24 February MANAGERIAL ECONOMICS a. Scatter plot Using excel software, the following scatter plot with a quadratic line fit is obtained.

The scatter diagram suggests a second-degree polynomial. This is because the points of the plot are evenly distributed along the fitted quadratic line of fit. The scatter diagram therefore suggests a function of the form: AVC= a + bQ+ cQ2

b. Estimated parameters for regression model

Parameters of the regression model can be estimated using excel. The following extract shows the regression coefficients as obtained from excel,

Regression statistics

Regression Statistics

Multiple R

0.855374

R Square

0.731665

Adjusted R Square

0.672035

Standard Error

121.9364

Observations

12

From the regression statistics and based on the high values of R square, 0.73, the predicted quadratic model explains a large percentage of the data. As a result, it can be assumed that the set of data significantly obeys the quadratic trend. Similarly, the following ANOVA table shows that there is a significant relationship between the model’s dependent variable and the explanatory variables, Q and Q2. This is due to the low probability value, 0.00269, which leads to the conclusion of existence of a significant relationship.

ANOVA table

ANOVA

df

SS

MS

F

Significance F

Regression

2

364875

182438

12.2701

0.00269

Residual

9

133816

14868.5

Total

11

498692

Based on the table of coefficients bellow, it can be concluded that the parameters for the model AVC = a + bQ + cQ2, are a = 2967, b = -4.28 and c = 0.003.

The model therefore assumes the following equation,

AVC = 2967 – 4.28 Q + 0.003 Q2

Table of coefficients

Coefficients

Standard Error

t Stat

P-value

Intercept

2967

335.38

8.84812

9.8E-06

X Variable 1

-4.28

1.5608

-2.7438

0.02271

X Variable 2

0.003

0.0017

2.06883

0.06849

c. Evaluation of the regression

The positive sign of the parameter c indicates that the average variable cost decreases with quantity before its value starts to increase as quantity increases.

d. Estimated costs functions

Average variable cost= AVC = 0.003 Q2 – 4.28 Q + 2967

Total variable cost= 0.003 Q3- 4.28 Q2+ 2967Q

Short run marginal cost= ∆(short run total cost)/ ∆quantity= 0.009 Q2 – 8.56 Q + 2967.

It is the derivative of total cost.

e. Minimum value for average variable cost

Minimum value of average variable cost is realized at an output level of 713 units.

This point is important in determining the shut down condition because it coincides with shut down point. Its analysis is important because average variable costs increases with increase in quantity beyond this point (McGuigan, Moyer and Harris, 2010).

f. AVC and SMC at 200 units

From the formulae above,

AVC= 0.003 (200)2 – 4.28 (200) + 2967

=120- 856+2967

= 2211

SMC= 0.009 Q2 – 8.56 Q + 2967

= 0.009(200)^2- 8.56(200)+2967

=360-1712+ 2967

=1615

g. Nature of AVC curve at 200 units

AVC is falling. This is because its value is higher that SMC. The observation is consistent with the identified shut down point of 713 units (McGuigan, Moyer and Harris, 2010).

h. The level at which SMC is equal to AVC

SMC is equal to AVC at 713 units of output. This is because the two variables intersect at this point.

i. Optimum level of production and maximum profit

The optimum production level is at 713 units.

The expected profit would be

713*2200-(20000+1027053)

=1568600-1047053

= $ 521547

j. When the market price is $ 1500

The optimal level is when,

SMC= 0.009 Q2 – 8.56 Q + 2967=1500

And 0.009 Q2 – 8.56 Q + 1467=0

Solving the equation leads to an optimal level of 224 or 727 units. 727 is however unrealistic.

Maximum profit would be given by,

224*1500- (20000+483573)

= -167573

The minimum loss would be $ 167573

k. Long run profitability of the industry

Profitability in the industry will reduce in the long run. This is because more firms will be attracted into the industry leading to lower selling price (McGuigan, Moyer and Harris, 2010).

Reference

McGuigan, J., Moyer, R., and Harris, F. (2010). Managerial Economics. Mason, OH: Cengage Learning

The scatter diagram suggests a second-degree polynomial. This is because the points of the plot are evenly distributed along the fitted quadratic line of fit. The scatter diagram therefore suggests a function of the form: AVC= a + bQ+ cQ2

b. Estimated parameters for regression model

Parameters of the regression model can be estimated using excel. The following extract shows the regression coefficients as obtained from excel,

Regression statistics

Regression Statistics

Multiple R

0.855374

R Square

0.731665

Adjusted R Square

0.672035

Standard Error

121.9364

Observations

12

From the regression statistics and based on the high values of R square, 0.73, the predicted quadratic model explains a large percentage of the data. As a result, it can be assumed that the set of data significantly obeys the quadratic trend. Similarly, the following ANOVA table shows that there is a significant relationship between the model’s dependent variable and the explanatory variables, Q and Q2. This is due to the low probability value, 0.00269, which leads to the conclusion of existence of a significant relationship.

ANOVA table

ANOVA

df

SS

MS

F

Significance F

Regression

2

364875

182438

12.2701

0.00269

Residual

9

133816

14868.5

Total

11

498692

Based on the table of coefficients bellow, it can be concluded that the parameters for the model AVC = a + bQ + cQ2, are a = 2967, b = -4.28 and c = 0.003.

The model therefore assumes the following equation,

AVC = 2967 – 4.28 Q + 0.003 Q2

Table of coefficients

Coefficients

Standard Error

t Stat

P-value

Intercept

2967

335.38

8.84812

9.8E-06

X Variable 1

-4.28

1.5608

-2.7438

0.02271

X Variable 2

0.003

0.0017

2.06883

0.06849

c. Evaluation of the regression

The positive sign of the parameter c indicates that the average variable cost decreases with quantity before its value starts to increase as quantity increases.

d. Estimated costs functions

Average variable cost= AVC = 0.003 Q2 – 4.28 Q + 2967

Total variable cost= 0.003 Q3- 4.28 Q2+ 2967Q

Short run marginal cost= ∆(short run total cost)/ ∆quantity= 0.009 Q2 – 8.56 Q + 2967.

It is the derivative of total cost.

e. Minimum value for average variable cost

Minimum value of average variable cost is realized at an output level of 713 units.

This point is important in determining the shut down condition because it coincides with shut down point. Its analysis is important because average variable costs increases with increase in quantity beyond this point (McGuigan, Moyer and Harris, 2010).

f. AVC and SMC at 200 units

From the formulae above,

AVC= 0.003 (200)2 – 4.28 (200) + 2967

=120- 856+2967

= 2211

SMC= 0.009 Q2 – 8.56 Q + 2967

= 0.009(200)^2- 8.56(200)+2967

=360-1712+ 2967

=1615

g. Nature of AVC curve at 200 units

AVC is falling. This is because its value is higher that SMC. The observation is consistent with the identified shut down point of 713 units (McGuigan, Moyer and Harris, 2010).

h. The level at which SMC is equal to AVC

SMC is equal to AVC at 713 units of output. This is because the two variables intersect at this point.

i. Optimum level of production and maximum profit

The optimum production level is at 713 units.

The expected profit would be

713*2200-(20000+1027053)

=1568600-1047053

= $ 521547

j. When the market price is $ 1500

The optimal level is when,

SMC= 0.009 Q2 – 8.56 Q + 2967=1500

And 0.009 Q2 – 8.56 Q + 1467=0

Solving the equation leads to an optimal level of 224 or 727 units. 727 is however unrealistic.

Maximum profit would be given by,

224*1500- (20000+483573)

= -167573

The minimum loss would be $ 167573

k. Long run profitability of the industry

Profitability in the industry will reduce in the long run. This is because more firms will be attracted into the industry leading to lower selling price (McGuigan, Moyer and Harris, 2010).

Reference

McGuigan, J., Moyer, R., and Harris, F. (2010). Managerial Economics. Mason, OH: Cengage Learning