# Dynamic Profit Maximization for a Monopolist

Dynamic Profit Maximization for a Monopolist

Assume that a monopolist faces the quasi-linear dynamic inverse demand function , which shifts over time . Assume also it produces with the nonlinear dynamic cost function . 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 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 (), average cost (), demand (), and marginal revenue ().

P(q,t)=80-q

0.03t

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0.2t

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TC(q,t)=180+80+60-0.5

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0.4q

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2

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0.1

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-0.2q

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MC

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