Example 2 The tables below show information about the demand and supply functions for a product. For both functions, or is the quantity and p is the price, in dollars. "Emu-MEE- P to st 53 4s 4s 35 at as "Emu-MEE- -II-----IE-I- a. Which is which? That is, which table represents demand and which represents supply? b. What is the equilibrium price and quantity"? c. Find the consumer and producer surplus at the equilibrium price. a. The rst table shows decreasing price associated with increasing quantity; that is the demand function. h. For both functions, or = 400 is associated with p = 40; the equilibrium price is $40 and the equilibrium quantity is 400 units. Notice that we were lucky here, because the equilibrium point is actually one ofthe points shown. In many cases with a table, we would have to estimate. c. The consumer surplus uses the demand function, which comes from the first table. We'll have to approximate the value of the integral using rectangles. There are 4 rectangles, and 1 choose to use left endpoints. 400 The consumer surplus = Hdemand) do (401400) E U [taxicab {s 11(1 un)+ (53](1 ou}+ (46](1 ee) (401.1400): T000. The consumer surplus is about $1000. The producer surplus uses the supply function, which comes from the second table. I choose to use lell endpoints for this integral also. Mill The producer surplus = (40)[400) Jlisupply] dq E [4o){400}-[{14]{100}+{211100}+(23]{100}+[33}neo} : 5400. The producer surplus is about $0400. 1.2 1.4 1.6 1.95 2.2 2.4 2.6 2.8 2.9 Note: there is some randomization in the aboye data to account for price uctuations. Make sure to check that you input the correct data in your device. Perform the following work . Assume that Supply has a quadrab'c relationship with the price. Find this relationship (the help buttons contain an article to compute trend-lines in Excel]: Slip] = I I Round your answer to 3 decimal places . Assume that the Demand has a quadratic relationship with the price. Find this relationship [the help button links to an article to compute trend-lines in Excel]: DEF] = I Round your answer to 3 decimal places . Use the trendlines to nd the price corresponding to the ec|u|ibrium price between supply and demand: 5 per gallon Round your answer to 2 decimal places