In Box-1, quantity Q and price P at the equilibrium point will be equal to A. Q=20 units and P=5 units B. Q=5 units and P=20 units C. Q=40 units and P=55 units D. Q=4 units and P=1... In Box-1, quantity Q and price P at the equilibrium point will be equal to A. Q=20 units and P=5 units B. Q=5 units and P=20 units C. Q=40 units and P=55 units D. Q=4 units and P=15 units
Understand the Problem
The question is asking to determine the equilibrium quantity (Q) and price (P) based on the provided demand and supply functions. The demand function is given as D = 40 - 4P and the supply function as S = SP - 5, where P is the price of the commodity. To solve this, we will set the quantity demanded equal to the quantity supplied and solve for Q and P.
Answer
Q = 4 units and P = 9 units.
Answer for screen readers
The equilibrium quantity (Q) is 4 units and the equilibrium price (P) is 9 units.
Steps to Solve
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Set Demand Equal to Supply To find the equilibrium price and quantity, set the demand function equal to the supply function: $$ 40 - 4P = SP - 5 $$
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Rearranging the Supply Function First, clarify the supply function: Let's express it clearly as ( S = P - 5 ) (assuming "SP" means just ( P )): So, we have: $$ 40 - 4P = P - 5 $$
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Combine Like Terms Rearranging the equation to isolate ( P ): $$ 40 + 5 = P + 4P $$
This gives: $$ 45 = 5P $$
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Solve for Price (P) Dividing both sides by 5 yields: $$ P = 9 $$
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Substituting P back to find Quantity (Q) Now substitute ( P = 9 ) back into either the demand or supply equation to find ( Q ): Using the demand function: $$ Q = 40 - 4(9) $$ $$ Q = 40 - 36 $$ $$ Q = 4 $$
The equilibrium quantity (Q) is 4 units and the equilibrium price (P) is 9 units.
More Information
In a competitive market, the equilibrium price is where the quantity demanded equals the quantity supplied. In this case, the price of 9 units leads to the demand being satisfied at a quantity of 4.
Tips
- Confusing the terms in the supply equation. Ensure correct interpretation of "SP" to avoid incorrect calculations.
- Not rearranging the equation properly. Double-check algebraic manipulations for errors.
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