I know I'm doing something wrong here b/c I keep getting ZERO for all of these? Should I be setting the marginal cost to match the price instead of 0?

Question #2

A Bacon Factory is located in a small town.Also in the town is a Water Park.The smell of the Bacon factory has adversely affected the Water Park such that it has put in air cleaning equipment to eradicate the odor created by the factory.

The cost function of the Bacon Factory is:

C_BF= 0.5B² + 3B+ (1 x)²

where B denotes the quantity of bacon produced annually and x denotes the quantity of pollutants that B creates in a given year. I suggest you assume x=1.

Thus, the Bacon Factory can limit production costs by eliminating its air scrubbers.However, the air pollution increases the costs for the water park W, whose cost function is:

C_WP = W² + 2x,

where W denotes the number of visitors (in millions) to the Water Park on an annual basis.Suppose that the unit price of admission to the water park is $16 and that the unit price of bacon is $33 per unit.

a)Compute the profit maximizing quantity of the Bacon Factory (B) and pollutant (x) produced by Bacon Factory B (assuming B behaves competitively in the output market, i.e., taking the price of Bacon as $32.50 (I used $33 as the price listed above)).Also, compute the Bacon Factory's (Firm B) profits.(Hint, set x=1).(8 Points)

a.Max Profit = $33B - 0.5B² - 3B - (1-x)²

i.30B-0.5B²=0

ii.B(30-0.5B)=0

iii.30=0.5B

iv.Quantity of Bacon =60

v.(1-x)² = 1 = quantity of pollution...also per your hint.

vi.Max Profit = $33(60) - 0.5(60)² - 3(60) - (1-1)²

1.1980-1800-180-0

2.$0

b)Compute the profit maximizing visits (represented by W) created by Firm W (assuming W behaves competitively in the output market, i.e., taking the price of visits as given). Notice that W does not choose x. Also, compute W's profits.(9 Points)

a.Max Profit = $16W - W² - 2x

i.16W - W² = 0

ii.W(16-W)=0

iii.16-W=0

iv.16=Water Park Visitors (in millions)

v.$16(16)-16²-2(1)

vi.256-256-2

vii.Max Profit = -$2M

c)Suppose now that the two firms B and W merge, creating B&W. The management of B&W now maximizes B&W's profits by appropriately choosing x, B, and W. Find the quantities of Bacon, Water Park Visits, and pollutants that the new firm produces. Also, find the profits of B&W.(3 Points)

a.Max Profit = $33B+$16W-0.5B² - 3B - W² - (1-x)² - 2x

i.30B-0.5B²=0

ii.B(30-0.5B)=0

iii.30=0.5B

iv.Quantity of Bacon =60

v.16W - W² = 0

vi.W(16-W)=0

vii.16-W=0

viii.16=Water Park Visitors (in millions)

ix.2(1x)2 = 2-2x-2 = 0Pollutants

b.Max Profit = $33B+$16W-0.5B² - 3B - W² - (1-x)² - 2x

i.$33(60) + 16(16)-0.5(60)²-3(60)-16²-0

ii.1980+256-1800-180-256-0

iii.Max Profit = $0