Answer:
q = 10 pounds = socially efficient amount of coffee for the company to roast.
Explanation:
Data Given:
Cost of Unroasted beans = 200 cents/pound.
Marginal Cost of roasting coffee beans = -10
+ 150
Cost neighbors willing to pay to stop shop operations = 5
Output selling price = 450 cents/pound
Required:
Amount of coffee to roast = ?
Solution:
As we know from the problem statement that it costs the company 200 cents/pound for the procurement of raw beans which are here termed as unroasted beans. Let's say it is the marginal cost of procuring.
Moreover, we know that marginal cost of roasted beans = -10
+ 150.
which is in the form of quadratic equation and will be solved for q to know the required answer.
Let's suppose X = marginal cost of unroasted beans.
Y = marginal cost of roasted beans.
MPC = Marginal Private cost
In order to calculate the marginal private cost, we need to add X+Y.
MPC = 200 + -10
+ 150
MPC = -10
+ 350
Now,
The total social cost which the neighbors are willing to pay = 5
In order to calculate marginal social cost, we need to differentiate the above equation.
MSC = d/dq5 = 10q
Finally,
Marginal Benefit = 450 cents/pound
For socially efficient amount = q =
MPC + MSC = Marginal Benefit
-10
+ 350 + 10
= 450
-10
+ 10
= 450-350
Solving for q,
= 100
taking square root on both sides,
q = +/-10.
Hence,
q = 10 pounds = socially efficient amount of coffee for the company to roast.