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REVISION

REVISION. Business Department. FALL 2013-14. Section A/type 1-Example- P rofit.

jana-mccormick
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REVISION

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  1. REVISION BusinessDepartment FALL 2013-14

  2. Section A/type 1-Example- Profit Samantha Jones has a job as a pharmacist earning $30,000 per year, and she is deciding whether to take another job as a manager of another pharmacy for $40,000 per year or to purchase a pharmacy that generates revenue of 200,000 per year. To purchase the pharmacy, Samantha would have to use her $20,000 savings and borrow another $80,000 at an interest rate of 10 % per year. The pharmacy that Samantha is contemplating purchasing has additional expenses of $80,000 for supplies, $40,000 for hired help, $10,000 for rent and $5000 for utilities. Assume that income and business taxes are zero and that repayment of the principal of the loan does not start before three years. a) What would be the business and economic profit if Samantha purchased the pharmacy?Should Samantha purchase the pharmacy? b) Suppose that Samantha expects that another pharmacy will open nearby at the end of three years and that this will drive the economic profit of the pharmacy to zero. What would the revenue of the pharmacy be in three years?c) What theory of profit would account for profits being earned by the pharmacy during the first three years of the operation? d) Suppose that Samantha expects to sell the pharmacy at the end of three years for $50.000 more than the price she paid for it and that she requires a %15 return on her investment. Should she still purchase the pharmacy?

  3. Section A/type 1-Example- Profit

  4. Section A/Type2-Graphical Soln/TR • Derive the avarage- and marginal- cost schedules. • (b) On the same set of axes, plot the total-, avarage- and marginal- cost schedules of part (a). • (c) With reference to your figure in part (b), explain the relationship among the total-, avarage- and marginal- cost curves in part (b). • (d) Calculate total revenue, marginal revenue and profit. • (e) On the same set of axes, plot total revenue, marginal revenue and profit (TR= 14Q-2Q2) • Solutions for parts d and e are not completed...

  5. Section A/Type2-Graphical Soln/TR

  6. Section B/Type1- Lagrangian • A company manufacturers commercial zippers ot two kind X and kind Y. Its production department estimatesbthat the avarage cost function of the firm is: • AC=X2 + 2Y2 -2XY-2X-6Y+20 • (a) The manager of the firm would like to know the level of output of zipper X and zipper Y at which the avarage cost of the firm is minimized and the level of of this minimum avarage cost. • (b)The firm expects an order of both zippers that will require it to produce a total output of 6 units of both kinds of zippers ( each unit may be a large number of zippers) and so the manager would also like to know how many of each type of zipper the firm must produce to minimize its avarage cost and what its minimum avarage cost would be if it receives the order. The manager gives this assignment to two researchers who use different methods to obtain answer. • (c) While the firm expects the order to be of 6 units, it may be as large as 7 units or small as 5 units. Determine the minimum avarage cost of the firm with these different order sizes. • (d) calculate and briefly interpret. • Part (d) is not computed...

  7. Section B/Type1- Lagrangian

  8. Section B/Type2- Price elas.. Suppose that GM’s Smith estimated the following regression equation for Chevrolet automobiles: Qc=100.000-100Pc+2.000N+50I+30Pf -1.000Pg+3A+40.000PI Where Qc= quantity demanded per year of Chevrolet automobiles Pc= price of chevrolet automobiles, in dollars N= population of the US, in millions I= per capita disposable income, in dollars Pf= price of ford automobiles, in dollars Pg= real price of gasoline, in cents per gallon A=advertising expenditures by Chevrolet, in per dollars per year PI= credit incentives to purchase Chevrolets, in percentage points below the rate of interest on borrowing in the absence of incentives.

  9. Section B/Type2- Price elas.. (a) Indicate the change in the number of Chevrolets purchased per year (Qc) for each unit change in the dependent or explanatory variables. Briefly explain. (b) Find the value of Qc if the avarage value of Pc= 9000$, N= 200 million, I= 10000$, Pf=8000$ , Pg=80 cents, A= $200.000 and if PI=1. Briefly explain. (c) Derive the equation for demand curve for Chevrolets and plot it. Briefly explain. (d) Find the price elasticity of demand at Pc= $8500. Briefly explain. (e) Calculate the income elasticity of demand betweenI= $10000 andI=$12000. Briefly explain.

  10. Section B/Type2- Price elas..

  11. Section C/type 1-Example-Regression Eqn • Use the information in the following table (Y is sales and X is Adv.Exp) and construct the regression equation.Briefly explain. • Plot the relevant graph and briefly explain. • Compute the standard error and t-value. Briefly explain whether t-value is significant at 5% level. • Compute the R2 and F-value. Briefly explain whether F-value is significant at 5% level. Also make a little comment on theR2.

  12. Section C/type 1-Example-Regression Eqn

  13. Section C/type 1-Example-Regression Eqn

  14. Section C/type 1-Example-Regression Eqn Yt^=7.60 +3.53 Xt = • Coefficient of Determination: is defined as the proportion of the total variation or dispersion in the dependent variable that explained by the variation in the explanatory variables in the regression. • In our example, COD measures how much of the variation in the firm’s sales is explained by the variation in its advertising expenditures.

  15. Section C/type 1-Example-Regression Eqn =45 • Hypotheses: • H0: 1 = 2 = … = k = 0 (No linear relationship) • H1: At least one i  0 ( At least one independent variable affects Y ) There is evidence that at least one independent variable affects Y.

  16. Section C/type 2-Example-Regression Eqn • Use the information in the following table. • a) Interpret the estimated coefficient of logk. • b) Conduct t-test and check AD is significant at 5% level. Briefly explain. • c) Conduct F-test and check whether it is significant at 5% level. Briefly explain • d) Conduct DW-test and check whether serial correlation exists or not. Briefly explain. • e) Conduct x2-test and check whether normality prblem exists or not. Briefly explain.

  17. Section C/type 2-Example-Regression Eqn

  18. Interpretation t-test (individual significance) Let’s first see the significance of each variable; n=39 k=6 and hence d.f.=39-6=33 =0.05 (our confidence level is 95%). With =0.05 and d.f.=33, ttab=2.045 Our Hypothesis are: Ho:s=0 (not significant) H1: s0 (significant) This is t- distribution and using this distribution, you can decide whether individual t-values (calculated or estimated) of the existing variables are significant or not according to the tabulated t-values as appears in the fig above.

  19. F-test (overall significance) Our result is F(6,33)=20.8432 k-1=5 and n-k=33 = 0.05 (our confidence level is 95%). With = 0.05 and F(6,33), the Ftab=2.34 Our hypothesis are Ho:R2s=0 (not significant) H1: R20 (significant)

  20. Normality: • Ho:ut=0 (residuals are not normally distributed) • H1:ut0(residuals arenormally distributed) • Our estimated result of LM version for normality is CHI-SQ(2)=1.28191, and the tabular value with 2 restrictions with = 0.05 is X2=5.991. • Since CHI-SQ(2)=1.28191< X2=5.991, the test result shows that the null hypothesis of normality of the residuals is accepted.

  21. Using the Durbin-Watson Statistic : No autocorrelation (error terms are independent) : There is autocorrelation (error terms are not) Inconclusive Reject H0(positive autocorrelation) Reject H0(negative autocorrelation) Accept H0 (no autocorrelation) 0 2 4 dL=1.104 dU=1.932 4-dU=2.09 4-dL=2.89

  22. Thanks

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