2 in a class of 120 students everybody would take two

2. In a class of 120 students, everybody would take two hamburgers if the price were zero, and no one would buy
hamburgers if the price were $4 or more. Assume that the class demand curve for hamburgers is linear and give
a formula
(a) describing quantity as a function of price (demand curve)
(b) describing price as a function of quantity (this is sometimes called the inverse demand curve)
Explain what the equation tells you for the demand for hamburgers when the price is $3 . 99.
3. Total revenue is a function of quantity and can be computed by R = price × quantity. Show that the total revenue
curve corresponding to the demand curve found in Problem 2 is quadratic. At what value does its maximum or
minimum occur?
4. A firm’s average cost function is given by the quadratic
y = x
2
- 20 x + 120
where y is average cost in dollars per unit of output. The output price is $10 per unit.
(a) Are there any output levels at which the firm just breaks even (i.e. price=average cost), if so find them.
(b) Sketch the average cost function and justify your answer to part (a) graphically.
(c) Over what range of prices does the firm make a loss at all output levels?
5. The demand curve for a product is given by q = 120000 - 500 p , and the supply curve is given by q = 1000 p for
0 ≤ q ≤ 120000, where price is in dollars.
(a) At a price of $100, what quantity are consumers willing to buy and what quantity are producers willing to
supply? Will the market push the prices up or down?
(b) Find the equilibrium price and quantity. Does your answer to part (a) support the observation that market
forces tend to push prices closer the equilibrium. Sketch a graph label the axis and show your reasoning on
a graph.
(c) Suppose a tax of 1 . 5 dollars per item is imposed on the supplier. Find the new eqilibrium price and quantity.
Support your answer graphically.
6. Let f and g be linear functions with equations f ( x ) = m
1
x + b
1
and g ( x ) = m
2
x + b
2
. Is f ◦ g also a linear
function. If so, what is the slope of its graph?