35. This exercise helps to explain the important relationship between demand curves and consumer surplus. Parts (b) (e) of this exercise refer to the following figure. 8 6 p = D(x) = (x -3)2 Price per Unit p (dollars) Section 4 The PUCara 2 02. which thiand Distance 0.5 1 1.5 2 2.5 3 Quantity x (in hundreds) a) Briefly explain why a demand curve is generally a decreasing function. b) The figure shows the demand curve p = (x - 3)' for a hypothetical product, where p is measured in dollars and the product is measure in hundreds of units. If the consumer is willing to pay $4 per unit, what does the shaded region in the figure represent and what is it's value? Economists define the consumer surplus (or utility) to be the area be- neath the demand curve p = D(x) and above line p = p*, where p* is some fixed price. We now compute the consumer surplus for p = $4. c) For the given figure and demand curve, use 4 rectangles to estimate the area beneath the function p = D(x) and above the interval [0, 1] on the x-axis. For your estimate, partition the interval [0, 1] into 4 subintervals