Economists apply the term elasticity to supply, demand, income, capital, labor, and many other variables in systems with input and output. In a few words, elasticity describes how changes in the input to a system are related to changes in the output. And because elasticity involves change, it also involves derivatives. Let's investigate the idea of elasticity as it applies to demand functions. It's a common experience that as the price of an item increases, the number of sales of that item generally decreases. This relationship is expressed in a demand function. Suppose a gas station has the linear demand function D = 1200 - 200p (see the graph below) where D is demand for gas (in gallons per day) as a function of price p (dollars per gallon). Demand (gal/day) 1200 D(p) = 1200 - 200p 600 W. 6 price ($/gal)Submit a discussion board post answering the following questions: According to this function, how many gallons of gas can the gas station owners expect to sell per month if the price is set at $4 per gallon? 1. Evaluate the derivative of the demand function with respect to price, D' . This is also referred to as marginal demand. Marginal demand describes how the quantity demanded changes with an increase in price. Since our demand function is linear, marginal demand is constant. 2. Explain why marginal demand is usually negative. That is, why would demand drop when prices increase? 3. What would you suspect to be the marginal supply of gas -- positive or negative? Explain why this is usually the case