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You are given the following supply and demand equation in the market for Tide Pods:๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘ =โˆ’2๐‘„๐ท+77๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘ =๐‘„๐‘†+11

Question

You are given the following supply and demand equation in the market for Tide Pods:๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘ =โˆ’2๐‘„๐ท+77๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘ =๐‘„๐‘†+11

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Solution

The given equations represent the demand and supply for Tide Pods in the market. The first equation is the demand equation and the second one is the supply equation.

Demand Equation: ๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘  = -2๐‘„๐ท + 77 Supply Equation: ๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘  = ๐‘„๐‘† + 11

To find the equilibrium price and quantity, we need to set the quantity demanded (๐‘„๐ท) equal to the quantity supplied (๐‘„๐‘†) and solve for the price (๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘ ).

Step 1: Set the two equations equal to each other:

-2๐‘„๐ท + 77 = ๐‘„๐‘† + 11

Step 2: Solve for ๐‘„๐ท or ๐‘„๐‘†:

-2๐‘„๐ท = ๐‘„๐‘† + 11 - 77 -2๐‘„๐ท = ๐‘„๐‘† - 66 Multiply by -1: 2๐‘„๐ท = -๐‘„๐‘† + 66 Divide by 2: ๐‘„๐ท = -0.5๐‘„๐‘† + 33

Step 3: Substitute ๐‘„๐ท in the demand equation:

๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘  = -2(-0.5๐‘„๐‘† + 33) + 77 ๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘  = ๐‘„๐‘† + 66 + 77 ๐‘ƒ๐‘‡๐‘–๐‘‘๐‘’๐‘๐‘œ๐‘‘๐‘  = ๐‘„๐‘† + 143

Step 4: Set this equal to the supply equation and solve for ๐‘„๐‘†:

๐‘„๐‘† + 143 = ๐‘„๐‘† + 11 Subtract ๐‘„๐‘† from both sides: 143 = 11 This is not possible, so there seems to be a mistake in the given equations. Please check the equations and try again.

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