Two dairy farmers, Albert and Brandon, share a common pasture. Each has a choice

Question

Two dairy farmers, Albert and Brandon, share a common pasture. Each has a choice of grazing 1 or 2 cows on the pasture. If 2 cows graze on the pasture, each will give 2500 gallons of milk per year. If 3 cows graze on the pasture, the grass will be thinner and each will give 1900 gallons of milk. If 4 cows graze on the pasture, the grass will have a hard time to recover, so each cow will give only 1000 gallons of milk. The market price of milk is $2 per gallon. If each farmer tries to maximize his revenue from selling milk, how many cows will each keep on the pasture? Construct a payoff matrix and find the Nash Equilibrium. What is the optimal number of cows to keep on the common pasture? Explain.

Explanation / Answer

If both of them choose to take two cows then they will get $5000 each. But if one chooses to go for one and other goes with 2 then 2nd person will get $7600 and 1st one will get $3800. And finally if both of them choose 2 they will get $4000 each. Since in last case both of them are getting higher amount than 2nd both will choose two cows. They will not choose 1 cow because there is a chance that if other take 2 then revenue will be much lower than 1,2 game.

So nash equilibrium is 2,2.

b) Optimum number of cows are 3, Since here their combined revenue will be much higher than other startagies.

1 2 1 5000,5000 3800,7600 2 7600,3800 4000,4000

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