Best for printing: 165demand.pdfDiscussion of Consumer's Demand and Willingness to SpendConsumer's Willingness to Spend is the Total amount A(q) that consumers are willing to spend
for q units. (A(q) dollars)
The consumer's demand function, p = D(q), is the rate of
change of A(q) wrt q; i.e., D(q) is the marginal
willingness to spend; units of D(q) are dollars/unit.
D(q0) ≈ A(q0 + 1) − A(q0),
so that D(q) approximates the price all consumers are willing to
pay for the (q0 + 1)st unit produced1.
Note that
A(q0) =
⌠ ⌡
q0
0
D(q) dq.
In the geometric context, ∫0q0 D(q) dq represents the
area under the graph of p = D(q), and above the interval
0 ≤ q ≤ q0 in the q-axis.
The Consumer's Surplus, CS(q0) is the total
willingness to spend − actual expenditure for q0 units
at price p0.
CS =
⌠ ⌡
q0
0
D(q) dq − p0 q0.
A supply function, p = S(q) is the price at which all
producers are willing to supply q units. It is generally
assumed that S(0) > 0, and that S(q) is an increasing function
of q. The text examples, S(q), are also concave upward, which
reflects a typical assumption that the total cost function,
C(q), is concave upward.
I (JL) think of S(q) as approximating the price required for the
production of the (q + 1)st unit,
The Producer's Surplus, PS(q0), is the
total consumer expenditure for q0 units at price
p0 - total amount producers receive for supplying q0
units.
PS = p0 q0 −
⌠ ⌡
q0
0
D(q) dq.
The analysis is usually done for p0 as the equilibrium
price where supply equals demand.
Solve the equation
D(q) = S(q).
The corresponding price, p0 = D(q0) = S(q0), is the equilibrium
price .
See Example 5.5.5 and Problems 5.5.15 - 5.5.19.
Another choice for p might be p = the price for which profit
is maximized. See Problems 5.5.33 and 5.5.34.