Homework #5
Econ 370 – Fall 2002
Hendrix
1.
Suppose the demand function for notebooks is expressed
1
D ( p, M )  Q  4  2 p 
M , where p is price and M is income. If income is
100
100 and price is 1, what is the income elasticity of demand for notebooks? What
is the price elasticity of demand?
2.
The demand function for tickets for a Rice football game is
D( p)  200,000  10,000 p . The athletic director wants to maximize the revenue
from selling tickets. Suppose that the stadium can hold 100,000 spectators (OK,
this is bigger than Rice Stadium, but it makes the numbers work out nicely.)
a.
b.
c.
d.
e.
f.
g.
3.
Write the demand function as a function of quantity (this is the
“inverse demand function”).
Using this inverse demand function, what is the expression for
total revenue? For marginal revenue?
Graph the inverse demand function.
What price and quantity give the athletic director maximum
revenue? (Remember, to find the maximum, differentiate the
function and set equal to zero.)
At this quantity, what is marginal revenue? Given the number for
marginal revenue, what is price elasticity of demand? (Remember
the formula for marginal revenue.)
Suppose that the team has had several winning seasons, so demand
is rising to a new level, D( p)  300,000  10,000 p . Ignoring
stadium capacity, repeat parts a through d with the new demand
function.
The quantity that maximizes revenue is greater than the seats
available. Given that the stadium can only hold 100,000, what
price and quantity should the athletic director enforce?
Suppose that in the market for butter, demand is expressed D( p)  120  4 p d and
supply is expressed S ( p)  2 p s  30 . Prices are measured in dollars per hundred
pounds and quantities are measured in hundreds of pounds.
a.
b.
c.
Algebraically and graphically show equilibrium price and quantity.
Suppose that a drought occurs and changes the supply function to
S ( p)  2 p s  60 . Algebraically and graphically show the new
equilibrium price and quantity.
In response to the drought, the government decides to pay a
subsidy of $5 per hundred pounds of butter to producers. If pd is
d.
e.
4.
the price paid by demanders for butter, what is the total amount
received by producers for each unit they produce? When the price
paid by consumers is pd , how much butter is produced?
(Remember, a subsidy is just the opposite of a tax.)
How can we solve for the equilibrium price paid by consumers,
give the subsidy program? What is the equilibrium price paid by
consumers? What is the equilibrium quantity?
Suppose the government had paid the subsidy to consumers rather
than producers? What would be the equilibrium net price paid by
consumers? What would the equilibrium quantity be?
Suppose that the demand for fish is expressed D( p)  200  5 p and the supply
curve is expressed S ( p)  5 p .
a.
b.
Graphically and algebraically find the equilibrium price and
quantity of fish.
What would happen to equilibrium price and quantity of fish if the
following occurred (think about inverse demand functions and the
equilibrium expressions for p and q given linear demand and
supply):
i)
ii)
iii)
iv)
c.
d.
e.
Demand becomes more steep?
Supply becomes more steep?
Demand shifts downward?
Supply shifts upward?
A quantity tax of $2 per unit sold is placed on fish. What does the
new equilibrium look like graphically? (price on the vertical axis is
the price paid by demanders)
In this new equilibrium, what is the price paid by demanders?
What is the price received by suppliers? What is the equilibrium
quantity sold?
What is the deadweight loss due to this tax? Calculate and show
graphically.