EE/GG 550

Lab Exercise 3

Two producers producing similar products are in a race for market dominance. At the beginning of the race each produces the same output quantity. We denote output by the two producers as Q1 and Q2, respectively. From these we can calculate the producer’s market share F1 and F2. We can also keep track of cumulative production, Z1 and Z2.

Each producer is free to adjust output as he or she wishes – but of course cannot exceed demand for the product – which would lead to lower prices. Assume that the more each producer produces of the product – the more experience that producer gains, and consequently, production costs decline per unit of output. Lower costs translate into lower prices P1 and P2, which, in turn, increase the attractiveness of the product – hence increasing demand.  The relationship between attractiveness (A) and price is linear and is shown in the graph below. However the relationship between cumulative production (Z1) and price (P1) is non-linear and indicates that as cumulative production increases, prices decline but at a diminishing rate. Draw your own graphical relationships that are similar to the ones shown here.

         

Assume that both producers have the same two curves. Also, assume there are always unknown, random influences operating on the market place and influencing the decision-making process of the producer. These you should capture by a random number varying between zero and one. The choice of how much to expand production from one period to the next in the light of these random influences and the market share is done in the following way. If the current market share of a producer exceeds the random number than this is taken by that producer as a sign that things are going well and thus production is increased above the previous level by a factor of (1+Ai), where i = 1, 2 stands for a particular producer. If the market share does not exceed the random number, then production is held steady, i.e. the new output level is equal to the previous output level.

TASK

1. Set up the model and plot in the same graph the market share of Producer 1 for 10 runs – run the model for 40 time-periods. Which producer will prevail in the market? Why?  Is it possible to know before running the model which one will prevail – how?  Could you change the initial conditions such that you know which producer will prevail?

2. Calculate each producer’s revenues and cumulative revenues. Then change the output expansion rule such that the increase in output is related to their revenues not production levels. Will the results change?

3. Modify the model to include some type of a negative feedback. For example, you could let the producers increase their production when they recognize that they fall back in the race. Choose one specification of negative feedback and explicitly state the assumptions that you make for your specification.  Will the ultimate outcome change – can you predict which producer will prevail in the market?