### Some Mathematics with A Pinch of Economics <!-- -->To run this page correctly, you need a more modern browser that understands JavaScript.<P><!--Beginning of JavaScript function dweeb() { f.ac4.value="70"; f.mc3.value="40"; f.vie.value="40"; f.viu.value="8400"; f.mb.value="40"; f.revenue.value="4800"; f.profit4.value="3600"; f.ps.value="2500"; f.cs.value="2500"; f.ep.value="50";f.eq.value="100"; f.comment.value=" "; f.comment.value=" "; f.comment2.value=" "; } function checkstart() { //var f=document.question; a3="Very good." if ((f.ac4.value==70)){f.B.src=imaged[2].src;} else {f.B.src=imaged[3].src;a3="For b, solve the equation P = 100 - .5(60)"} if (f.mc3.value==40.){f.A.src=imaged[2].src;} else {f.A.src=imaged[3].src;a3="To answer a, solve the equation Q = 200 - 2(80)"} f.comment9.value=a3; } function checkanswer() { //var f=document.question; a1="Very good."; if (f.vie.value==40){f.G.src=imaged[2].src; } else {f.G.src=imaged[3].src;a1="For g, value in exchange is price."} if (f.viu.value==8400){f.F.src=imaged[2].src; } else {f.F.src=imaged[3].src;a1="For g, value in use is the total of consumer surplus plus total revenue of sellers."} if (f.mb.value==40){f.E.src=imaged[2].src; } else {f.E.src=imaged[3].src;a1="For e, the demand curve shows marginal benefit. What is the most someone would pay for the 120th unit?"} if (f.revenue.value==4800){f.D.src=imaged[2].src; } else {f.D.src=imaged[3].src;a1="For d, revenue is sales (120) multiplied by price (40)."} if (f.profit4.value==3600){f.C.src=imaged[2].src; } else {f.C.src=imaged[3].src;a1="For c, consumer surplus is the top triangle under the demand curve in the picture. The base is 120 and the height is 60."} if (f.profit4.value==7200){a1="For c, The area of a triangle is one half base times width."} f.comment.value=a1; } function check() { //var f=document.question; a2="Very Good!"; if (f.ps.value==2500) {f.K.src=imaged[2].src; } else {f.K.src=imaged[3].src;a2="For d, the producer surplus is also a triangle with a base of 100 and a height of 50. It is the area above the supply curve and below the horizontal line indicating price."} if (f.cs.value==2500) {f.J.src=imaged[2].src;} else {f.J.src=imaged[3].src;a2="For c, the consumer surplus is a triangle with a base of 100 and a height of 50."} if (f.ep.value==50) {f.I.src=imaged[2].src; } else {f.I.src=imaged[3].src;a2="For b, solve P = 100-.5(100)."} if (f.eq.value==100) {f.H.src=imaged[2].src;} else {f.H.src=imaged[3].src;a2="For a, solve .5Q = 100 - .5Q"} f.comment2.value=a2; } //-End of JavaScript- -->

 CyberEconomics tries to hide the mathematics that lurks behind much of economics, and instead it tries to give you the intuition and commonsense of economic ideas and theories. For those who miss the mathematics, here is a simple problem just for you. Demand curves can be given in the form of an equation, such as: Quantity Demanded = 200 - 2(Price) which can also be written as: Price = 100 -.5(Quantity Demanded) This is a straight-line demand curve, which is easy to work with mathematically. Real-world demand curves are unlikely to ever be so simple. a) If Price equals 80, what would Quantity Demanded be? b) If Quantity Demanded equals 60, what would Price be? \$ Do not enter the dollar sign with your answers. Below is a graph showing this demand curve. Suppose that in this market price is 40 and quantity demanded is 120 as in the graph. Recall that the formula for area of a rectangle is height times width, and the formula for area of a triangle is one half height times width. c) What is the consumer surplus? \$ d) What is the revenue going to sellers? \$ e) What is the marginal benefit of the 120th unit? \$ f) What is value in use when 120 are produced? \$ g) What is the value in exchange in this market? \$ Do not enter the dollar sign with your answers. (The following questions add a supply curve, and you might want to read the sections on producer surplus and how both consumer surplus and producer surplus appear on a supply and demand graph before you attempt these questions.) Suppose that there is a supply curve in this market that has the equation: Quantity Supplied = 2Price. What will equilibrium quantity be? What will equilibrium price be? \$ At this equilibrium, what will consumer surplus be? \$ At this equilibrium, what will producer surplus be? \$