**Question 3 **

Finding the best response for Beta is as follows;

The demand function for Beta whines is

QB=9000-100PB+40PA

Fin the function of the price in the above equation

The price for Beta’s product can be equated as follows;

PB= (9000+40PA-QB)/100=90+2/5PA-1/100QB

Find the marginal revenue of the firm;

The marginal revenue (MRA) also can be equated as;

MRB=90+2/5PA-1/50QB

From the information, the marginal cost for Beta Winery is = $10 per bottle.

The marginal cost is uniform to the marginal revenue as follows

90+2/5PA-1/50QB= 10

QB=50* (-10+90+2/5PA) =4000+20PA

Equating the quantity function to the demand function of Beta Winery to find the best response function.

The best response function in this case is

PB=1/5PA+50

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**Question 4 **

At equilibrium the two functions of the two firms can equate as follows;

PA=1/2PB+110

PB=1/5PA+50

Equating PA=1/2PB+110 to PB=1/5PA+50, gives PB=80

Equating the PB=80 into the first equation, you get that PA=150

If PA=$150 and PB=$80, then the equation QA=200-150+80=130 bottles and QB=9000-i.e. 100*80+40*150=7000bottles.

We need to find the profit of the two firms.

To determine the profit of:

Alpha: 130 bottles *$150per bottle -$6000(fixed costs) =$13500

Beta: 7000bottles *$80per bottle-$10000(fixed costs) = $550000.

From this calculations we can inference that at equilibrium, Alpha and Beta charge a bottle of wine in $150 per bottle and $80 per bottle. In conclusion, Alpha and Beta can sell 130 bottles and 7000bottles respectively. Alpha and Beta’s profits are $13500 and $550000 respectively.

**Question 5 **

Using the Lerner index (L= (P-MC)/P) to measure market power.

P is for the price of the product and MC is a marginal cost of the product. In this case, P is the equilibrium price, (P=$150) for Alpha and (P=$80) for Beta. Marginal cost is $20 per bottle for Alpha and $10 per bottle for Beta. So substituting the values gives;

L Alpha= (150-20)/150=0.867

L Beta= (80-10)/80=0.875.

From the above L Beta has lower Lerner index than L-Alpha. From the above calculation, we see that Beta has greater market power as it has lower marginal cost.

**Question 6 **

An increase in Beta’s Winery’s fixed cost to $100000 the equilibrium price won’t change. This is because the equilibrium function is related to the amount of other product. But not to the fixed costs. (Varian, 2014).

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