2. Demand can be expressed in two forms: direct demand, where Q is on the left and P on the right, or inverse demand, where P is on the left and Q on the right. Sometimes it's easier to work with direct demand and supply; other times it's easier to work with the indirect versions. So we need to be able to recognize the two, sometimes even switch between them. Here, suppose that aggregate (market) inverse demand for gasoline in a local market is given by P = = D(Q) = 5 - Q/200, where Q is the gallons of gasoline bought per year and P is the price of a gallon in dollars. Note that here D(Q) is a price in dollars. The inverse supply of gasoline is given by P = S(Q) = Q/800. Here S(Q) is also a price in dollars. a. Construct a carefully labeled diagram showing these two equations. The axis labels will be Q on the horizontal and P on the vertical axis. b. Compute the equilibrium quantity and price of gasoline. c. Compute consumer surplus at the equilibrium. d. Due to an international crisis, the supply curve for gasoline shifts upward by 50cents per gallon, to S'(Q) = 0.5 + Q/800. Compute the new equilibrium quantity and price after the change in supply. Compute the new consumer surplus and also the reduction in consumer surplus due to the upward shift in supply.
2. Demand can be expressed in two forms: direct demand, where Q is on the left and P on the right, or inverse demand, where P is on the left and Q on the right. Sometimes it's easier to work with direct demand and supply; other times it's easier to work with the indirect versions. So we need to be able to recognize the two, sometimes even switch between them. Here, suppose that aggregate (market) inverse demand for gasoline in a local market is given by P = = D(Q) = 5 - Q/200, where Q is the gallons of gasoline bought per year and P is the price of a gallon in dollars. Note that here D(Q) is a price in dollars. The inverse supply of gasoline is given by P = S(Q) = Q/800. Here S(Q) is also a price in dollars. a. Construct a carefully labeled diagram showing these two equations. The axis labels will be Q on the horizontal and P on the vertical axis. b. Compute the equilibrium quantity and price of gasoline. c. Compute consumer surplus at the equilibrium. d. Due to an international crisis, the supply curve for gasoline shifts upward by 50cents per gallon, to S'(Q) = 0.5 + Q/800. Compute the new equilibrium quantity and price after the change in supply. Compute the new consumer surplus and also the reduction in consumer surplus due to the upward shift in supply.
Chapter4: Demand, Supply, And Market Equilibrium
Section: Chapter Questions
Problem 25P
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Question
Transcribed Image Text:2. Demand can be expressed in two forms: direct demand, where Q is on
the left and P on the right, or inverse demand, where P is on the left and Q
on the right. Sometimes it's easier to work with direct demand and supply;
other times it's easier to work with the indirect versions. So we need to be
able to recognize the two, sometimes even switch between them. Here,
suppose that aggregate (market) inverse demand for gasoline in a local
market is given by
P =
= D(Q) = 5 - Q/200,
where Q is the gallons of gasoline bought per year and P is the price of a
gallon in dollars.
Note that here D(Q) is a price in dollars. The inverse supply of gasoline is
given by
P
=
S(Q) = Q/800.
Here S(Q) is also a price in dollars.
a. Construct a carefully labeled diagram showing these two equations. The
axis labels will be Q on the horizontal and P on the vertical axis.
b. Compute the equilibrium quantity and price of gasoline.
c. Compute consumer surplus at the equilibrium.
d. Due to an international crisis, the supply curve for gasoline shifts upward
by 50cents per gallon, to S'(Q) = 0.5 + Q/800. Compute the new
equilibrium quantity and price after the change in supply. Compute the new
consumer surplus and also the reduction in consumer surplus due to the
upward shift in supply.
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