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Short Assignment Requirements

Student Number to be used in the assignment9314093141

Assignment Description

Course 7310 – Assignment 2                                                                        Fall 2016


This assignment will be presented in class November 28. It consists of computing and analyzing the optimal price- and advertising decisions for firm over three periods. Use under ”Downloads” file Course7310_Assignment2_2016.XLSM”. The mean decisions of the other firms (competition) are in cells B36 – D37. The price- and advertising decisions (cells B16 – D17) that give maximal equity after period 3 (cell D31) shall be determined. We would also like to know the difference between monopoly and competition with fixed/determined decision, Nash-equilibrium decisions, the same prices decision for the firms in three period, the results of sensitive analysis, and patterns of paths to and in Nashequilibrium decision for different start values. 


1.      Carefully document and comment the formulas in the Excel-file and the VB-code!  Use the Solver to compute the optimal price- and advertising decisions for the studied firm as a monopoly (“Number of firms” in cell B2 =1) and with respect to the mean decisions of the other firms (see how this number is calculated below). Hint: Maximize D31 by changing B16:D17. Use different start values and show the results in a table. 

2.      Compute Nash-equilibrium where the optimal decisions of the studied firm is the same or similar to the mean decisions of the other firms. Do it manually by using the Solver repeatedly or compose a macro with the Solver or with Grid Search (see Note* below) to obtain optimal prices and advertising for three periods. Assign these decisions to the mean of the other firms, and optimize again. Continue until the optimal decisions are same as or similar to the decisions of the other firms. These decisions approximate the Nash-equilibrium. Also, calculate this equilibrium path when prices must be the same in all periods (advertising can be different).

3.      Conduct a sensitivity analysis for the maximal equity of the studied firm as a monopoly, in competition, and at Nash-equilibrium for the number of firms (determined below) for the parameters: Market size, price elasticity, mean price and advertising of the other firms in the same market. The analysis should be conducted for -10% and +10% of parameters and the decisions of the other firms. Make tables and Spider-graphs etc, to display the results.

4.      *Paths to and in Nash-equilibrium decisions for the three periods may reveal what decisions can be expected of the firms. Calculate and analyze these paths for different start decisions, and also when prices have to be the same in all periods. Use ginerics or any other method to obtain patterns. Make tables and graphs to display the results. Hint: Start with analyzing one path.

5.      Conclusions. Make graphs showing optimal decisions, profits in each period, and the equity after three periods for a monopoly, when the firm is competing with other firms (the decisions given in the workbook), and also the Nash equilibrium. Also, for Nash-equilibrium, make graphs and tables, that show and analyze the path for these decision. Comment on the results. 


Work in pairs of two students. Some exceptions can be made so that individuals can work on their own.

The number of other firms in the market (cell B2) shall be calculated with: 

Mod(studentnumber1 * studentnumber2 / 10000; 3) + 3. Before noon December 5, a workbook named Course7310_Assignment2_studentnumber_studentnumber.xlsm shall be sent to .... Subject in email: Course7310, Assignment 2, surname, studentnumber, surname, studentnumber


Note*: Nash-equilibrium can be calculated manually, or by composing a macro in Visual Basic. The Grid Search method can be used to compute the optimal price- and advertising decisions of firms. A macro needs to then have 6 nested FOR loops, 3 for price and 3 for advertising. Hint: The macro code in Exercise 2 may useful, for starters, as it uses Grid Search for prices in three periods. Advice: use only three alternatives/steps for each loop as it may take long time run the macro with many steps. The Nash-equilibrium can also be solved by running Solver in Macros in Visual Basic multiple times. Select Tools/References. Browse (down) to folder that contains SOLVER.XLAM and Open it. Any macro, if used, shall be in VB-code in a module in the workbook and also copied to a sheet. Any macro(s) shall work and be well documented. 

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