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Dynamic Profit Maximization for a Monopolist

​
time
7
marginal cost
average costs
demand
marginal revenue
profit
Assume that a monopolist faces the quasi-linear dynamic inverse demand function
P(q,t)=80
0.03t
e
-q
0.2t
e
, which shifts over time
t
. Assume also it produces with the nonlinear dynamic cost function
TC(q,t)=180
-t
e
+80
0.4q
0.5
t
e
+60
2
q
-t
e
-0.5
0.1
t
-0.2q
e
. The function reveals both economies of scale (decreasing average costs) and learning effects (downward shifts of average and marginal costs) over time. The optimal quantity
Q
decisions made by the firm and the prices paid by consumers change over time, leading to profit changes. This Demonstration shows the profit surface in 3D as a function of output and time, and plots marginal cost (
MC
), average cost (
AC
), demand (
D
), and marginal revenue (
MR
).
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