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Solving Economic Equations Using Quadratic Formula and Analyzing Demand & Supply Functions

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This tutorial covers the application of the quadratic formula in various economic scenarios, including finding equilibrium price and quantity, evaluating cost functions, and determining profit maximization outputs. Key questions addressed involve quadratic equations with different parameters and their implications for total revenue and cost functions. The IS-LM model is also introduced, with detailed examples on consumption, investment, and money demand equations. This comprehensive guide aids students in understanding complex economic principles through practical examples.

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Solving Economic Equations Using Quadratic Formula and Analyzing Demand & Supply Functions

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  1. ECON 103Tutorial 3 Rob Pryce www.robpryce.co.uk/teaching

  2. Question 1a Use the quadratic formula to solve: X = 40 X = 2.5

  3. Question 1b Use the quadratic formula to solve: Question 1b Question 1a

  4. Question 1c Use the quadratic formula to solve: a=12 b=90 c=-48

  5. Question 1d • Find the output value at which total revenue is £600 if a firm’s demand schedule is

  6. Question 1e • A firm faces the average cost function . At which value(s) of is average cost equal to 40?

  7. Question 2a • Given the following supply and demand functions for a good, find the equilibrium price and quantity: Solve using quadratic formula P = 6 (or -7.2 which we ignore) Q = 16

  8. Question 2a

  9. Question 2b Given the following inverse supply and demand functions for a good, find the equilibrium price and quantity: Solve using quadratic formula, or double to get q = 10 P = 70

  10. Question 3a P Never touches y axis Never touches x axis Q

  11. Question 3b

  12. Question 3c • Does this hyperbolic demand function have constant elasticity with respect to price? Elasticity is constant at -1

  13. Question 3c – Another Proof

  14. Question 3d • Now assume that the inverse demand function changes to . • Does this hyperbola intersect the quantity axis (the horizontal axis)? P 3a Q 3d -10

  15. Question 3d • Now assume that the inverse demand function changes to . • How does the equilibrium of the market change? Q = 4.14 P = 38.28

  16. Question 4a • If total fixed costs are 30, variable costsper unit are q + 3, and the demand function is • p + 2q = 50 • Show that the associated profit function is:

  17. Question 4b • If total fixed costs are 30, variable costsper unit are q + 3, and the demand function is • p + 2q = 50 • Find the break-even levels of output (when total profit = 0) = 0 Use quadratic formula Q = 2/3 or Q = 15

  18. Question 4b • If total fixed costs are 30, variable costsper unit are q + 3, and the demand function is • p + 2q = 50 • Find the level of output where total profit is maximised.

  19. Question 5a • What are the values parameter can assume to make this function suitable for representing demand?

  20. Question 5b • What are the values parameter can assume to make this function suitable for representing supply?

  21. Question 5c • Take natural logarithms on both sides to linearise this nonlinear function

  22. Question 6 Consumption: C = 200 + 0.7(Y-T) Investment: I = 150 + 0.25Y – 1000r Government Spending: G = 250 Taxes: T = 200 Money Demand: L = 0.6Y – 8000r Money Supply: Ms = 1600 Y = C + I + G

  23. Finding the IS equation Y = C + I + G Y = 200 + 0.7(Y – T) + 150 + 0.25Y – 1000r + 250 Y = 200 + 0.7Y – 0.7T+ 150 + 0.25Y – 1000r + 250 T = 200 Y = 200 + 0.7Y – 140+ 150 + 0.25Y – 1000r + 250 Y = 460 + 0.95Y – 1000r 0.05Y = 460 – 1000r Y = 9200 – 20,000r 20,000r = 9200 – Y r = (9.2/20) – (Y/20,000) r IS Y

  24. Finding the LM Equation r LM IS Y

  25. Equilibrium in IS-LM Model

  26. Any Questions? Email: r.pryce@lancaster.ac.uk Web: www.robpryce.co.uk/teaching Office Hour: Thursday 1pm Charles Carter C floor (near C7)

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