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Mathematics in Business and Economics

Conclusion

The purpose of this resource has been to provide an overview of some of the main operations and principles that you will have to cope with in following an introductory economics course. This makes no claim to be definitive but does allow the novice to be able to remind themselves about the fundamentals that underpin a quantitative methods course in economics.

Below is a series of questions typical of those you might come across in the first few weeks of a quantitative methods course in economics for you to work through. Remember, the best method of ensuring you understand is to keep working through examples but think as you go along what the signs, etc. in the questions signify in terms of what the graph might look like, the nature of the relationship being expressed and so on.

Further Questions

  1. Draw the graph of the following functions. Calculate the break-even point and then confirm your result by working out the answer. TR = 90q - 2q2, and TC = 15 + 10q - 2.5q2 + 0.5q3
  2. Find the formula for the marginal revenue and marginal cost for the respective functions in question 1 above.
  3. Given the demand schedule P = 30 - 0.75q, calculate the point elasticity of demand when price = £2, £4 and £6
  4. Given the demand schedule p = 370 - 0.3q and the supply schedule p = 50 + 0.6q, find the equilibrium market price and quantity.
  5. In the question above, what would happen to this market price and quantity if the demand changed by 15 at all prices and the price elasticity fell to 0.4?
  6. A firm faces the total cost function TC = 8q3 - 35q2 + 45q + 25 and the revenue function TR = 270q - 4q2. Use two different methods to calculate the output level at which profit will be maximised.
  7. Given the conmsumption function Y = 0.4Y + 300 find the equilibrium level of income and state what injection of investment would be needed to generate an income level of 2,000.
  8. Given the TC function TC = 5q2 + 8q + 15, find the marginal and average cost and then state what these would be at the values q = 5 and q = 7.
  9. Given the production function 10K0.25 + L0.4 = 2,200 find the marginal rate of technical substitution and state what this value is when K = 260 and L = 120.
  10. A non-linear demand schedule is given as p = 550 - 0.25q2. What is the output level which will maximise sales revenue?

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