Transcript Math Review
Micro Tools Review Key Terms/Tasks • • • • • • • • • 1. Plotting coordinates 2. Vertical intercept 3. Horizontal intercept 4. Slope 5. Ceteris paribus: how relates 6. Tangency 7. Independent variable 8. Dependent variable. 9. Solving equations. Graph of a Demand Curve Demand for Concert Tickets Point on Curve a Ticket Price Ticket Demand $250 0 b $200 40 c $150 80 d $100 120 e $50 160 f $0 200 Relate to Demand Theory • Demand curve: Shows quantity demanded as a function of price so that Qd is the dependent variable and P is the independent variable. Qd = fn(P). • Ceteris Paribus Assumption: “Other Things Equal” : graph is twodimensional and everything ELSE related to quantity demanded OTHER than price is held constant. • Note: c.p.factors, draw new line. • Law of Demand: Negative relationship between quantity demanded and price. Line slopes down. Further Details • For folks with math background: with this graph, economists put the independent variable (price) on the vertical axis and the dependent variable (quantity demanded) on the horizontal axis. This is opposite to what is done in math, and will affect how you calculate the slope off of the equation. • The shape of the demand curve is the SLOPE. Since the curve is downward-sloping, we say the slope is negative. Calculating Slope of Demand Curve • Slope of Demand curve always negative as curve is drawn down to right. • Calculate slope as movement from one point to another. Slope = rise/run Slope = (P) / (Qd) • Using previous graph drawn: Slope = (200-150)/(40-80) = 50/-40 = 5/-4 = -1.25. Slope using Algebraic Expression • Equation for a demand curve: Qd = a – bP Qd = 8 – 2P • • • • Qd = quantity demanded P = price See negative relationship Slope of demand curve: Need P/Q. • See: -b = Q/P Slope = -1/b = -1/2 Intercepts • Intercepts are where the line hits the vertical and horizontal axis. • Vertical intercept: answers question—what is price when Qd=0? Can show on graph and solve for using equation. • Horizontal intercept: answers question—what is Qd when P=0? Can show on graph and solve for using equation. Calculate Intercepts Using Equation • Use equation for demand curve: Qd = a – bP Qd = 8 – 2P • Solve for vertical intercept: Set Qd=0 and solve for price. 0 = 8-2P 2P=8 P=4 (see = a/b in general equation) • Solve for horizontal intercept: Set P=0 and solve for Qd. Qd=8 – 2*0 Qd=8. (see = a in general equation) Measuring Slope of Nonlinear Curve • Slope of a nonlinear curve is NOT a constant, so slope will be different at each different point along the curve. • To measure slope of nonlinear curve: – Pick a particular point; – Draw line tangent to the curve at that point; – Calculate slope of that tangent line. – Intercepts useful here. • Note that tangent means touches at one point. Slope of Nonlinear Curve Solving Equations • Two skills: – 1) Given an equation and a price, solve for quantity (example below). – 2) Given two equations, solve for equilibrium price and quantity (example to come in later chapter). • Example for # 1: Qd = a – b P 15 = 20 – 1*P. Solve for P. In-Class Exercise POINT Video Price Video Qd a $60 0 b 50 3 c 40 6 d 30 9 e 20 12 f 10 15 g 0 18 Tasks to Complete • • • • • Draw graph Describe relationship Calculate slope Identify both intercepts Write equation for the line