Problem Set 1 -- Supply and Demand
1. Assume that the United States demand curve for corn is
QD = 80 - 2P
where P is the price of corn (in dollars per bushels) and QD is the quantity of demanded of corn ( in billions of bushels) and that
QS = 20 + 4P
is the supply curve for corn where QS is the quantity of corn supplied (in billions of bushels).
a. What are the equilibrium price and quantity?
At equilibrium, QD =QS
80 - 2P= 20 + 4P
6P = 60
P = $10
Qd = 80 – 2(10) = 80 -20 = 60 billion bushels
Qs = 20 + 4(10) = 60 billion bushels
b. What is the slope of the Demand?
The slope of the demand is -2 which implies an inverse relationship between price and quantity demanded. This indicates that if price will go up by a dollar unit, quantity demanded will fall by 2 units.
c. What is the slope of the Supply?
The slope of the supply is +4which implies a direct relationship between price and quantity supplied. This indicates that if price will go up by a dollar unit, quantity suppliedwill rise by 4 units.
d. Suppose the market price is below the equilibrium price. What would you expect to happen to the market price and the QD and the QS as the market adjusts to the disequilibrium? Why?
If the market price is set below the equilibrium price, more will be demanded than supplied, (Qd>Qs). This creates a shortage of the goods in the market. The amount of shortages will cause buyers to bid up the price in order to acquire the goods. Competition among buyers will bid up the price. Price will go up until shortages are eliminated.
e. Suppose the supply shifts to
QS = 30 + 4P
Has the slope of the supply changed? Why or why not?
No, the slope of the supply remained the same. Only the intercept changed. The rate of change in quantity supplied remained at 4 units for every dollar increase or decrease.
At equilibrium, QD = QS
80 - 2P = 30 + 4P
6P = 50
P = $8.33
Qs = 30 + 4(8.33) = 63.33 billion bushels
2.Following the collapse of the subprime mortgage market in 2008, the price of lumber plummeted from roughly $290 per thousand board feet to less than $200 per thousand board feet. New home construction also declined markedly. Draw graphs showing what you believe happened in these markets and explain why.
As the subprime mortgage market collapse, the demand for new homes declined.Price per unit of houses will fall.
Demand for new homes
As the prices of new homes declined, sellers become less keen in constructing and selling new homes. Therefore, demand for lumber, an input for home construction also declined.
Demand for lumber
3.Suppose that the price of a commodity declines from one month to the next and that more is bought in the second month. Draw three diagrams one showing that the demand could have increased, a second diagram showing that the demand could have decreased, and a third showing that demand might not have changed. [pic]
4.Draw a diagram to show what would happen if the government imposed a ceiling on the retail price of gasoline. Why do some advocates of price controls also recommend rationing?
If the government set a price ceilingon the retail price of gasoline. More gasoline will be demanded than supplied. This creates a gasoline shortage which may be addressed by a rationing system in order that everyone will get a fair share of the commodity.Shortages often result to long queues and rationing schemes such as the first-come first-served basis, payment of reservation fees, and even lottery.
Moreover, price ceiling encourages hoarding. This in turn leads to the proliferation of the black market where people succumb to higher prices in order to acquire...