95年政大企管 第三題 a commondity is introduced with an initial price of $5 per unit, and t months later the price is p(t) dollars per unit. A study indicates that at time t the demand for the commondity will be D(t)=3+10e^-0.01t thousand units will be supplied. Suppose that at each time, price is changing at a rate equal to 2% of shortage D(t)-S(t). a. Set up and solve a differential equation for the unit price p(t). b. At what time is the unit price the largest? What is the maximum unit price and the corresponding supply and demand? c. What happens to the price in the "long run" (as t→∞） --

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