This is about economic solution.There are 2 regions but they were given by different each other function of demand and supply.1.First question is we won't sell these products on both regions and you can't transport the product each other.So please find the equilibrium price,equilibrium quantity,shortage and surplus of goods on one by one.Functions were written below.
a.Q(demand)=50-0.5P
Q(supply)=-10+P (first region)
b.Q(demand)=120-P
Q(supply)=-20+P (second region)
2.If you can transport the product to these 2 regions cheapestly,please find the equilibrium quantity on these 2regions one by one.If you can't transport any product from first to second region,who can get a profit from them?.Who can't get a profit from these condition?
But this condition is abstraction,so this condition is unreliable on real life.Please think abstractly,so maybe we can solve them.But I have not good idea.Do you have any solution?
To find the equilibrium price, equilibrium quantity, shortage, and surplus of goods in each region, we can set the demand equal to the supply for each region.
1. First Region:
a. Demand function: Q(demand) = 50 - 0.5P
b. Supply function: Q(supply) = -10 + P
To find the equilibrium price and quantity in the first region, we equate the demand and supply functions:
50 - 0.5P = -10 + P
Simplifying the equation, we get:
1.5P = 60
P = 40
Substituting the equilibrium price back into either the demand or supply function, we can find the equilibrium quantity:
Q = -10 + 40
Q = 30
Therefore, the equilibrium price in the first region is $40, and the equilibrium quantity is 30. To determine if there is a shortage or surplus, we compare the equilibrium quantity with the quantities demanded and supplied at that price:
At a price of $40:
Demand: Q(demand) = 50 - 0.5(40) = 50 - 20 = 30
Supply: Q(supply) = -10 + 40 = 30
Since the quantities demanded and supplied are equal to the equilibrium quantity, there is neither a shortage nor a surplus in the first region.
2. Second Region:
a. Demand function: Q(demand) = 120 - P
b. Supply function: Q(supply) = -20 + P
To find the equilibrium price and quantity in the second region, we equate the demand and supply functions:
120 - P = -20 + P
Simplifying the equation, we get:
2P = 140
P = 70
Substituting the equilibrium price back into either the demand or supply function, we can find the equilibrium quantity:
Q = -20 + 70
Q = 50
Therefore, the equilibrium price in the second region is $70, and the equilibrium quantity is 50. To determine if there is a shortage or surplus, we compare the equilibrium quantity with the quantities demanded and supplied at that price:
At a price of $70:
Demand: Q(demand) = 120 - 70 = 50
Supply: Q(supply) = -20 + 70 = 50
Since the quantities demanded and supplied are equal to the equilibrium quantity, there is neither a shortage nor a surplus in the second region.
Now, let's consider the scenario where the products can be transported between the two regions.
1. Transported between both regions:
In this scenario, the equilibrium quantity will be determined by the combined demand and supply functions of both regions. We sum up the individual demand and supply functions:
Q(demand) = (50 - 0.5P) + (120 - P)
Q(supply) = (-10 + P) + (-20 + P)
To find the equilibrium quantity, we equate the demand and supply functions:
(50 - 0.5P) + (120 - P) = (-10 + P) + (-20 + P)
Simplifying the equation, we get:
-1.5P = -160
P = 106.67 (rounded to two decimal places)
Substituting the equilibrium price back into the combined demand or supply function, we can find the equilibrium quantity:
Q = (50 - 0.5(106.67)) + (120 - 106.67)
Q = (50 - 53.335) + (120 - 106.67)
Q = -3.335 + 13.33
Q = 9.995 (rounded to two decimal places)
Therefore, the equilibrium price when goods can be transported between both regions is approximately $106.67, and the equilibrium quantity is approximately 9.995. The quantity is rounded to two decimal places.
Now, let's analyze who can get a profit and who can't in this scenario:
Assuming the costs and pricing remain the same in each region, if the equilibrium price when goods can be transported is higher than the equilibrium price in the first region ($106.67 > $40), then the first region can get a profit by selling its goods in the second region.
However, the second region cannot get a profit because the equilibrium price when goods can be transported ($106.67) is lower than the equilibrium price in the second region ($70).
In summary, the first region can get a profit when goods can be transported between both regions, while the second region cannot obtain a profit in this scenario due to the lower equilibrium price.