Quantitative Methods for Economics and Business

Quantitative Methods for Economics and Business Winter 2022 Assignment 1 Due: Monday, Jan. 31st, 9PM

Total /30

 

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  1. Solve the following equations. (1 mark each)

a) 10π‘₯ + 16 = 4π‘₯ βˆ’ 8π‘₯ + 2

b) (π‘₯ + 12)(π‘₯ βˆ’ 3) = 0

c)   π‘₯ βˆ’ 3π‘₯  =2

6       12       3

d) π‘₯βˆ’2 βˆ’ 7π‘₯ = 0

5

e)    5π‘₯  = 3π‘₯+8

f)   (π‘₯ βˆ’ 6)2 = 121
 

g) βˆšπ‘₯ + 1 = 13

 

h) βˆš 2π‘₯ π‘₯+2+ 4 = 4

 

  1. For the demand function P = 500 – 2Q
    1. What is the slope? What are the intercepts? (2 marks)
    2. What is the quantity demanded when P = 100? (1 mark)
    3. Graph the demand function. (1 mark)
    4. What is the elasticity of demand when π‘ƒ1 = 100 and π‘ƒ2 = 120? (2 marks)
  2. Given the supply function P = 50 + 3Q
    1. What is the slope? What is the vertical intercept? (2 marks)
    2. What is the quantity supplied when P = 500? (1 mark)
    3. Graph the supply function. (1mark)
  3. The demand and supply functions for a good are given by:

𝑃𝑑 = 50 βˆ’ 3𝑄𝑑

𝑃𝑠 = 14 + 1.5𝑄𝑠

  1. Calculate the equilibrium P and Q. (2 marks)
  2. Calculate π‘„𝑑 and π‘„𝑠 when P = 38. (1 mark)
  3. Calculate π‘„𝑑 and π‘„𝑠 when P = 20. (1 mark)
  4. The demand and supply functions for a good are given by:

𝑃𝑑 = 1620 βˆ’ 20𝑄𝑑

𝑃𝑠 = 960 + 40𝑄𝑠

  1. Calculate the equilibrium P and Q. (2 marks)
  2. Graph the supply and demand functions on the same graph. (2 marks)
  3. Suppose the government imposes a tax of 120. Calculate the equilibrium price and quantity when the tax is imposed. (2 marks)
  4. Calculate the amount of tax paid by the consumer and the amount of tax paid by the producer. (2 marks)

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