Subject Code : ECO331
Assignment Task:

Task:

Question 1 (30 marks) A. After two pivot steps, the tableau of a profit maximization linear program assumes the following form: X1 X2 S1 S2 S3 Constant Row 1 0 0 1 -0.4 -0.47 26.67 Row 2 1 0 0 0.4 -0.20 440 Row 3 0 1 0 0 0.67 533.33 Indicators 0 0 0 14 26.5 42,066.67 (i) Is this an optimal tableau? Why? [2 marks] (ii) What are the values of ? ? ? [6 marks]

(iii) Interpret the last four values of row 5. [4 marks]

(iv) How many choice variables would its dual program contain? Why? [3 marks]

B. Consider the Sequential-move capacity expansion game between Toyota and Honda. Honda moves first. Toyota BL BS DB Honda BL 0 ,0 12, 8 15, 9 BS 8, 2 16, 16 20, 15 DB 9, 18 15, 17 18, 16 Where BL, BS and DB represent build large, build small and don’t build, respectively.

(i) Find the Nash Equilibrium of this game [4 marks]

(ii) Express the game above in its extensive form [5 marks]

(iii) Using the Subgame-perfect Nash Equilibrium concept, find the equilibrium capacity strategy for Toyota and Honda [6 marks] 3

Question 2 (30 marks) A dietitian has recommended that you take a minimum of 4 units of vitamin A, 6 units of Calcium, 3 units of Protein and 1 unit of Zinc each day. Assume that your diet consists of three types of meals. Brand I costs P550 and supplies units of vitamin A, 2 units of Calcium, 4 units of Protein and 3 units of Zinc. Brand II costs P700 and supplies 4 units of vitamin A, 1 unit of Calcium, 2 units of Protein and 1 unit of Zinc. Brand III costs P200 and supplies 2 units of vitamin A, 3 units of calcium, 1 unit of Protein and 2 units of Zinc.

(i) Express the least-cost combination of nutrients that will guarantee you the daily requirements as equations and inequalities {hint: set up the LPP for this problem}. [2 marks]

(ii) Obtain the corresponding dual to the primal in

(i) above [2 marks]

(iii) Use the simplex method to solve the dual problem in

(ii) above. [6 marks] (iv) Obtain the optimal values of the primal problem in

(i) from the solution of its dual in

(iii) above. [4 marks]

B. In the beer promotion game below, two bottle stores have received a new brand of beer and each one of them can advertise it on Btv. When the advert appears on Btv, 10,000 beer drinkers will purchase the beer per week. The cost of advertising the beer is that while the one who advertises pays for the ad at Btv, the other bottle store will use its financial resources to hire more cashiers. The payoffs from this game are presented in the table below. Tops Advertise Wait Liquarama Advertise 5, 1 4, 4 Wait 9, -1 0, 0 (i) Identify the dominant strategy for Liquarama [2 marks]

(ii) Identify the dominant strategy for Tops [2 marks]

(iii) Use the dominant strategy equilibrium concept to find the equilibrium strategies for Liquarama and Tops. [3 marks]

(iv) Use the iterated dominance strategy equilibrium concept to find the equilibrium strategies for Liquarama and Tops. [3 marks]

4 C. Saltco has dominated the salt-producing industry in Botswana for years, earning significant monopoly profits. Recently a new company, Matswai, has used new technology to become a potential entrant into the salt industry. However, Matswai knows that before it enters the industry it will have to invest P80million in a new plant to incorporate the new technology. Matswai also knows that Saltco can either respond to Matswai’s entry by keeping its high price, or engage in a price war to try to push Matswai out. The profit pay-off that describes the entry/no entry is shown in the table below, with Saltco’s profits (Pm) shown on the left in each square. Matswai Entry No entry Saltco High price 100, 20 200, 0 Low price 60, -20 80, 0 Suppose Saltco threatened a price war (i.e., low price) in an attempt to discourage Matswai from entering the salt industry. Do you think Saltco’s threat is a credible one? Why or why not?

 

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  • Posted on : March 31st, 2019

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