Suppose the market demand Q_d (in tonnes) and market supply Q_s (in tonnes) are both linear functions in market price P (dollars in thousands) given by: Q_d=-5P+68, and Q_s=3P-10. What are the price P and trade quantity Q at equilibrium? Round your answer to 3 decimal places. Question 4 Answer a. P=9.750, Q=38.750 b. P=19.250, Q=9.750 c. P=9.750, Q=19.250 d. none of the others e. P=38.750,Q=9.750
Question
Suppose the market demand Q_d (in tonnes) and market supply Q_s (in tonnes) are both linear functions in market price P (dollars in thousands) given by:
Q_d=-5P+68, and
Q_s=3P-10.
What are the price P and trade quantity Q at equilibrium? Round your answer to 3 decimal places.
Question 4 Answer
a. P=9.750, Q=38.750
b. P=19.250, Q=9.750
c. P=9.750, Q=19.250
d. none of the others
e. P=38.750,Q=9.750
Solution
In order to find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for P. This is because at equilibrium, the quantity demanded equals the quantity supplied.
So, we have:
-5P + 68 = 3P - 10
Solving this equation for P gives:
8P = 78
P = 78 / 8
P = 9.75 (rounded to three decimal places)
Substituting P = 9.75 into either the demand or supply equation will give us the equilibrium quantity. Let's substitute it into the demand equation:
Q_d = -5(9.75) + 68
Q_d = -48.75 + 68
Q_d = 19.25 (rounded to three decimal places)
So, the equilibrium price P is 9.75 and the equilibrium quantity Q is 19.25. Therefore, the correct answer is:
c. P=9.750, Q=19.250
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