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+ cQ2b. Estimated parameters for regression modelParameters of the regression model can be estimated using excel. The following extract shows the regression coefficients as obtained from excel, Regression statisticsRegression StatisticsMultiple R0.855374R Square0.731665Adjusted R Square0.672035Standard Error121.9364Observations12From 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 tableANOVA dfSSMSFSignificance FRegression236487518243812.27010.00269Residual913381614868.5Total11498692 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 Q2Table of coefficients CoefficientsStandard Errort StatP-valueIntercept2967335.388.848129.8E-06X Variable 1-4.281.5608-2.74380.02271X Variable 20.0030.00172.068830.06849c. Evaluation of the regressionThe 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 functionsAverage variable cost= AVC = 0.003 Q2 – 4.28 Q + 2967Total variable cost= 0.003 Q3- 4.28 Q2+ 2967QShort 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 costMinimum 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 unitsFrom the formulae above, AVC= 0.003 (200)2 – 4.28 (200) + 2967=120- 856+2967= 2211SMC= 0.009 Q2 – 8.56 Q + 2967= 0.009(200)^2- 8.56(200)+2967=360-1712+ 2967=1615g. Nature of AVC curve at 200 unitsAVC 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 AVCSMC 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 profitThe optimum production level is at 713 units. The expected profit would be 713*2200-(20000+1027053)=1568600-1047053= $ 521547j. When the market price is $ 1500The optimal level is when, SMC= 0.009 Q2 – 8.56 Q + 2967=1500And 0.009 Q2 – 8.56 Q + 1467=0Solving 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)= -167573The minimum loss would be $ 167573k. Long run profitability of the industryProfitability 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). ReferenceMcGuigan, J., Moyer, R., and Harris, F. (2010). Managerial Economics. Mason, OH: Cengage Learning