The demand and supply functions of a good are given by{ P = 3 QD + 12P = −5QS + 20where P denotes the price, QD the quantity demanded and QS the quantitysupplied.(a) Determine the equilibrium price and quantity.(b) Sketch the demand and supply functions on the same graph. Label theaxes and the intercepts clearly
Question
The demand and supply functions of a good are given by{ P = 3 QD + 12P = −5QS + 20where P denotes the price, QD the quantity demanded and QS the quantitysupplied.(a) Determine the equilibrium price and quantity.(b) Sketch the demand and supply functions on the same graph. Label theaxes and the intercepts clearly
Solution
(a) To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied. This means we set QD = QS.
So, we have:
3QD + 12 = -5QS + 20
Since QD = QS, we can write this as:
3Q + 12 = -5Q + 20
Solving for Q gives:
8Q = 8
Q = 1
Substituting Q = 1 into either the demand or supply equation will give us the equilibrium price. Let's use the demand equation:
P = 3(1) + 12 = 15
So, the equilibrium price is 15 and the equilibrium quantity is 1.
(b) To sketch the demand and supply functions, you would draw two lines on a graph. The y-axis represents the price (P) and the x-axis represents the quantity (Q).
The demand function is a line with a slope of 3 and a y-intercept of 12. This means it starts at the point (0,12) and for every unit increase in Q, P increases by 3.
The supply function is a line with a slope of -5 and a y-intercept of 20. This means it starts at the point (0,20) and for every unit increase in Q, P decreases by 5.
The point where these two lines intersect is the equilibrium point, which we calculated to be (1,15).
Similar Questions
You are given the following economic functions:pQpQ219;313621Where P is the market price for a particular good and Q is the quantity.i) Identify with reasons the demand and supply functions. (3 Marks)ii) Explain the negative intercept of the second function2Q above
The demand and supply functions for different firms are given belowi) Qd = 200 – 2PQs= - 20 + 2Pii) Qd = 51 – 3PQs = -4 +8PDetermine the equilibrium price and equilibrium quantity for each firm
1. In a particular market, demand and supply curves are defined by the following equations: P=100– 0.5QD QS= -200 + 2P where, P is the price in pounds, QS is the quantity supplied and QD¬ is the quantity demanded. (a) What is the equilibrium price and quantity? [5 marks] (b) What is the price elasticity of supply at a price of £35? [5 marks]
In a supply-demand diagram with price measured on the vertical axis and quantity on the horizontal, the market equilibrium is found where the supply and demand curves . (Insert a single word.)
In a competitive market the demand curve is given by P = 120–2q and supply by P = q. What are the equilibrium price and quantity traded?Group of answer choicesP* = 60, q* = 60P* = 40, q* = 80P* = 40, q* = 40P* = 20, q* = 40None of the above.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.