The demand functions of the 3 commodities: A, B and C are given as QdA = 20 - 3PA + PB + pc, QdB = 30 + PA - 5PB and QdC = 15 + PA3PC and the corresponding supply functions also QsA= 9PA, QsB = 30PB- 3 and QsC = 3PC - 1, then find equilibrium price and quantity of each ?

Question

Visualize a symbolic representation of the equilibrium of supply and demand across three commodities, A, B, and C. Show a minimalistic scenario with three graph charts, each chart representing one commodity. On each chart, depict two intersecting lines signifying the supply and demand functions, where the intersection symbolizes the equilibrium point. Make sure the charts or graphs are simple and without any text. Please use a neutral and appealing color palette.

The demand functions of the 3 commodities: A, B and C are given as QdA = 20 - 3PA + PB + pc, QdB = 30 + PA - 5PB and QdC = 15 + PA3PC and the corresponding supply functions also QsA= 9PA, QsB = 30PB- 3 and QsC = 3PC - 1, then find equilibrium price and quantity of each ?

Answer 1

For commodity A:

QdA = QsA
20 - 3PA + PB + PC = 9PA
12PA = PB + PC + 20
PA = (PB + PC + 20)/12

For commodity B:
QdB = QsB
30 + PA - 5PB = 30PB - 3
PA + 5PB = 33
PA = 33 - 5PB

For commodity C:
QdC = QsC
15 + PA = 3PC - 1
PA = 3PC - 16

Now we can substitute the expressions for PA in terms of PB and PC, and solve for PB and PC:
(PB + PC + 20)/12 = 33 - 5PB
PB + PC + 20 = 396 - 60PB
61PB + PC = 376
3PC - 16 = (PB + PC + 20)/12
36PC - 192 = PB + PC + 20
35PC + PB = 212

Solving these two equations simultaneously, we get:
PB = 4.25
PC = 62.75

Substituting these values into the equations for PA, we get:
PA = 10.25

Therefore, the equilibrium price and quantity for each commodity are:
Commodity A PA = 10.25, QA = QsA = 92.25
Commodity B PB = 4.25, QB = QsB = 12.75
Commodity C PC = 62.75, QC = QsC = 187.25

Answer 2

Note: It is important to check that these values indeed satisfy the demand and supply equations for each commodity.

Answer 3

To find the equilibrium price and quantity for each commodity, we need to set the quantity demanded equal to the quantity supplied for each commodity. Let's solve them one by one.

1. For commodity A:
Quantity demanded (QdA) = Quantity supplied (QsA)
20 - 3PA + PB + PC = 9PA

Simplifying the equation:
12PA - PB - PC = 20

2. For commodity B:
Quantity demanded (QdB) = Quantity supplied (QsB)
30 + PA - 5PB = 30PB - 3

Simplifying the equation:
5PB - PA = 33

3. For commodity C:
Quantity demanded (QdC) = Quantity supplied (QsC)
15 + PA + 3PC = 3PC - 1

Simplifying the equation:
PA - 2PC = -16

To solve the system of equations, we can use any method such as substitution or elimination. Here, we will use the elimination method.

First, let's eliminate the variable PC from the equations for commodities A and C:

Multiply the equation for commodity C by 3 and add it to the equation for commodity A:
3(PA - 2PC) + (12PA - PB - PC) = 60 + 20

Simplifying:
36PA - PB = 80

Now, let's eliminate the variable PA from the equations for commodities B and the newly obtained equation:
Multiply the equation for commodity B by 36 and subtract it from the updated equation:
36(5PB - PA) - (36PA - PB) = 198 - 80

Simplifying:
179PB = 118

Finally, solve for PB:
PB = 118/179

Substitute the value of PB into the equation for commodity B to find PA:
5(118/179) - PA = 33

Simplifying:
PA = 5(118/179) - 33

Now that we have found the values of PA and PB, we can substitute them into any of the original equations to find the value of PC. Let's use the equation for commodity C:
PA - 2PC = -16

Substitute the values into the equation:
(5(118/179) - 33) - 2PC = -16

Simplifying:
PC = (5(118/179) - 33 + 16) / 2

Now, substitute the values of PA, PB, and PC into the equations for quantity demanded to find the equilibrium quantity of each commodity.

For commodity A:
QdA = 20 - 3PA + PB + PC

Substitute the values:
QdA = 20 - 3(5(118/179) - 33) + (118/179) + [(5(118/179) - 33) - 2((5(118/179) - 33) + 16) / 2]

Simplify the expression to find QdA.

Similarly, substitute the values of PA, PB, and PC into the equations for quantity demanded for commodities B and C to find QdB and QdC.

Once you find the values of QdA, QdB, and QdC, you will have the equilibrium quantities for each commodity.

Answer 4

To find the equilibrium price and quantity for each commodity, we need to set the quantity demanded equal to the quantity supplied and solve the resulting system of equations.

For commodity A:
QdA = QsA
20 - 3PA + PB + PC = 9PA

Simplifying the equation:
-3PA + PB + PC = 9PA - 20
12PA = PB + PC + 20

For commodity B:
QdB = QsB
30 + PA - 5PB = 30PB - 3

Simplifying the equation:
6PB - PA = 33

For commodity C:
QdC = QsC
15 + PA + 3PC = 3PC - 1

Simplifying the equation:
PA = -16

We now have three equations:
12PA = PB + PC + 20
6PB - PA = 33
PA = -16

Solving this system of equations, we find that the equilibrium price and quantity for each commodity are:

Commodity A:
PA = -16
QdA = QsA
20 - 3(-16) + PB + PC = 9(-16)
68 + PB + PC = -144
PB + PC = -212

Commodity B:
PA = -16
QdB = QsB
30 + (-16) - 5PB = 30PB - 3
-21 - 5PB = 30PB - 3
35PB = -18
PB = -18/35

Commodity C:
PA = -16
QdC = QsC
15 + (-16) + 3PC = 3PC - 1
-1 + 3PC = 3PC - 1
0 = 3PC

We can see that commodity C has no equilibrium price and quantity.

To summarize:

Commodity A:
Equilibrium price (PA) = -16
Equilibrium quantity (QdA) = QsA = 68
Equilibrium price of commodity B (PB) = -18/35

Commodity B:
Equilibrium price (PB) = -18/35
Equilibrium quantity (QdB) = QsB = -21

Commodity C:
There is no equilibrium price and quantity as the equation for commodity C does not have a solution.

Note: It is important to check the given equations and simplify them correctly to ensure accurate results.