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Objective: To use the concept of elasticity of demand to determine an appropriate tuition level for the University. Problem Description: This is a continuation of Math 117 laboratory exercise # 2. In that exercise, you were required to develop supply and demand curves from sample data and to calculate the market equilibrium point. The data consisted of two data points each for the supply and demand curves. The data were credit hours and cost per credit hour. In this exercise, we'll modify the demand data slightly and use the data points: 62000 credits hours will he demanded (registered for by students) when the tuition cost is $900 per credit hour and 122000 credit hours will be demanded when the tuition cost is $400. So you have the data points (p,q) ( 900, 62000) and (400, 122000). You are to use the concepts of elasticity to assist in selecting the tuition rate that will ensure the best possible total revenue. When possible for elasticity type problems, it is convenient to express quanity as a function of price. Recall: The formula for elasticity is given by E = - (plq)(dqidp). Step 1. Your data is on the next sheet under p and q. The price is shown to be from 100 to 1400 on the given chart. Then, use the data points given above to develop the expression that represents demand (number of credit hours) as a function of price. Recall: the equation of a line is of the form y = mx+b (where m is the slope and b is the y-intercept). In our case, the y-variable is q and the x-variable is p. Fill in the rest of the values for q using your formula, and make sure it agrees with the two vaiues you're given before going on! Step 2. Find the derivative of quantity with resprect to price and use it to nd the formula for the elasticity for demand, E. Step 3. In column 0, ll in the values for E and graph the coefcient of elasticity over your range of the price variable. Step 4. Develop (in column D) and graph the Total Revenue function, R. (Recall: R = qp.) From the graph, estimate the costlcredit hour that will maximize the Total Revenue. Find the elasticity at that value of p. Step 5. Find the costicredit hour gure that produces a unity coefcient of elasticity. That is, use GoalSeek to find the value of p for which E = 1. As your conclusion, make a guess as to the relationship between the value of the coefcient of elasticity for a demand function and a value of price that maximizes the Total Revenue. p q E R Step1:m= 100 The demand "curve" equation is: Q= (5pm each) 200 300 400 500 000 700 Step 2: dqldp= (Spts each) 000 900 1000 1100 1200 1300 1400 ( each of six questions 2pts each ) Step 3: (Fill in) The demand is elastic for p between and . The demand is inelastic for p between and Thus, for p = 300, would you expect that a small increase in price would result in a large decrease in demand Why? How about p = 800? Why? . Step 4: Using the chart at the left with only the orginal p values it appears that R is maximized at about p = At that value of p, E (2 questions at 3 pls each) Step 5: E: 1 when p = Show the use of "goal seek" Conclusion from steps 4 and 5: (20pts)