5. Suppose the demand and supply curves for a product are given by QD = 500 2P Q
ID: 1196461 • Letter: 5
Question
5. Suppose the demand and supply curves for a product are given by QD = 500 2P QS = 100 + 3P a. Graph the supply and demand curves. b. Find the equilibrium price and quantity. c. If the current price of the product is $100, what is the quantity supplied and the quantity demanded? How would you describe this situation, and what would you expect to happen in this market? d. If the current price of the product is $150, what is the quantity supplied and the quantity demanded? How would you describe this situation, and what would you expect to happen in this market? e. Suppose that demand changes to QD = 600 – 2P. Find the new equilibrium price and quantity, and show this on your graph.
Explanation / Answer
The figure for the reference is given at the end of the solution.
a.
The demand function is
QD = 500 - 2P
Write it in inverse form.
P = 250 - QD/2
When P is zero then the quantity demanded is 500 [=500 - 2(0)]. When quantity demand is zero then the price is 250 [=250 - (0/2)]. Using this information, graph the demand curve as shown in the figure (given at the end of the solution).
The suply function is
QS = - 100 + 3P
Write it in inverse form.
P = (QS + 100)/3
When P is 40 then the quantity supplied is 20 [= -100 + 3(40)] units. When P is 50, then the quantity supplied is 50 [= -100 + 3(50)] units. Using this information, draw the supply curve as shown in the figure.
b. The equilibrium price is that price where the quantity demanded and quantity supplied are equal.
Qd = QS
500 - 2P = -100 + 3P
5P = 600
P = $120
At this price, the quantity demanded and quantity supplied are 260 units.
c) When price is $100, then quantity supplied is 200 units and quantity demanded is 300 units. That is, when price is $100, buyers won't be able to buy all they want to buy. So they will bid the price up until the equilibrium is reached.
d) When price is $150, then quantity supplied is 350 units and quantity demanded is 200 units. That is, when price is $150, sellers won't be able to sell all they want to sell. So they will bid the price down until the equilibrium is reached.
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