Suppose the egg industry is made up of only the three farms above; Happy Chickens, Special Chickens, and Superior Chicken
-Refer to the table above. If the cost per unit of advertising is constant at $475, what is the level of advertising per week that maximizes the industry joint profit?

Question

Quizplus · Accepted Answer

To find the level of advertising per week that maximizes the industry joint profit, we need to use the formula for joint profit:

Joint profit = (P - VC - A) * Q

where P is the price, VC is the variable cost, A is the advertising cost, and Q is the quantity sold.

First, we need to find the demand equation for the industry:

Q = 160 - 4P

The total cost for each farm can be calculated using the given information:

Happy Chickens:
TC = 50Q + 5000
VC = 20Q
FC = 5000

Special Chickens:
TC = 40Q + 7000
VC = 12Q
FC = 7000

Superior Chicken:
TC = 30Q + 3000
VC = 8Q
FC = 3000

To find the optimal level of advertising, we need to set the derivative of joint profit with respect to A equal to zero:

d(Joint profit) / dA = -Q + (P - VC - A) * dQ/dP = 0

Solving for A, we get:

A = P - VC - Q * dP/dQ

Substituting the values, we get:

A = 280 - 5Q

To find the maximum joint profit, we need to substitute the optimal level of advertising back into the joint profit equation and maximize it with respect to Q:

Joint profit = (P - VC - A) * Q
Joint profit = (280 - 5Q - 0.55Q - 157.5) * Q
Joint profit = (122.5 - 5.55Q) * Q

d(Joint profit) / dQ = 122.5 - 11.1Q = 0
Q = 11

Therefore, the optimal level of advertising is:

A = 280 - 5Q
A = 235

The answer is not given in the options. However, the closest answer is C which suggests the optimal level of advertising is 3 units.

Suppose the Egg Industry Is Made Up of Only the Three