Layout and explain the logic of the following simple Hotelling model illustrating the equilibrium intertemporal price trajectory of a perfectly competitive mining industry. Use the following assumptions:

• The mining industry is perfectly competitive. • The cost of resources is impact by geological events over time. • The demand for the product increases linearly as a function of time. • The industry is in long-run equilibrium, but the resource cost remains constant over time. In the Hotelling Model, perfect competition in the mining industry leads to a linear intertemporal price trajectory––meaning that prices change linearly as a function of time. This is because the extraction cost remains fixed over time, while the demand for the product increases linearly as a function of time. Thus, as time moves forward, the industry adjusts its output of the commodity up or down to meet the increasing demand and maintain equilibrium in the long run. Graphically, this can be written as follows: P(t) = P(0) + a*t where P(t) is the price of the commodity at time t, P(0) is the initial price at time 0, and a is the rate of increase in price as a function of time. As mining resources become scarcer over time, the cost of producing the commodity rises accordingly. This allows the firms in the industry to capture any cost savings due to the geological events in their prices. Thus, the increasing demand coupled with the increasing costs of the resource lead to a continuously increasing price of the commodity as time moves forward. Ultimately, perfect