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LEARNING BY DOING SOLVING EQUATIONS 1. Solve the following pairs of equations simultaneously a. Q = -20+3P Q = 220 –5P b. Q = -45 + 8P Q = 125 – 2P c. Q+32-7P=0 Q-128+9P=0 d. 13P – Q = 27 Q+4P-24 = 0 2. Find the intercepts and slopes of each of the equations in (a) to (d) 3. Graphically plot the each pair of equations in (a) – (d) with P on the vertical axis and Q on the horizontal axis: 4. (a) Define Consumer Surplus. (b) Calculate consumer surplus in the following graph. D P S P* Q Q* 5 Goods X and Y are complements in production and substitutes in consumption. Given that the price of good Y rises, explain what happens to the equilibrium quantity of X and the equilibrium price of X as a result of this price increase in Y. Draw a demand and supply graph of the market for X. 6. Starting from a position of equilibrium, the price of leather decreases. The demand for beef remains unchanged. What happens to the equilibrium price and the equilibrium quantity of beef? Assume that beef and leather are complements in production. Illustrate your answer with a demand & supply graph for Beef. Use the demand and supply model discussed in class to perform your analysis. 7. Pg. 62 exercise 1 8. Pg62 exercise 2 9. Pg 62 exercise 3 10. Pg 62 exercise 4 11. What is the difference between arc elasticity and point elasticity? a. Write down the definition for arc own price elasticity. b. Write down the definition for point own price elasticity. 12. Write down the formula for own price point elasticity. Now manipulate the formula to express elasticity in terms of the slope of the demand curve. 13. For a linear demand graph like P = a – bQ show the following: a. = at the vertical intercept b. = 0 at the horizontal intercept c. = 1 at the midpoint of the demand line. 14. Given that >1 at a point on the demand curve will a 1 % change in price result in a greater than 1% change in quantity? Why? 15. Given that < 1 at a point on the demand curve will a 1 % change in price result in a greater than 1% change in quantity? Why? 16. (a)Consider the following price and quantity data on the demand for X. Is good Y a substitute or a complement in consumption? How can you tell? Price of X 10 5 Quantity Demanded of X 5 15 Price of Y 2 3 (b) Consider the following price and quantity data on the supply of X. Is good Y a substitute or a complement in production? How can you tell? Price of X 10 5 Quantity Supplied of X 5 15 Price of Y 2 3