Quantitative Methods for Economics and Business Winter 2022 Assignment 1 Due: Monday, Jan. 31st, 9PM
Total /30
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- Solve the following equations. (1 mark each)
a) 10π₯ + 16 = 4π₯ β 8π₯ + 2
b) (π₯ + 12)(π₯ β 3) = 0
c) π₯ β 3π₯ =2
6 12 3
d) π₯β2 β 7π₯ = 0
5
e) 5π₯ = 3π₯+8
f) (π₯ β 6)2 = 121
g) βπ₯ + 1 = 13
h) β 2π₯ π₯+2+ 4 = 4
- For the demand function P = 500 β 2Q
- What is the slope? What are the intercepts? (2 marks)
- What is the quantity demanded when P = 100? (1 mark)
- Graph the demand function. (1 mark)
- What is the elasticity of demand when π1 = 100 and π2 = 120? (2 marks)
- Given the supply function P = 50 + 3Q
- What is the slope? What is the vertical intercept? (2 marks)
- What is the quantity supplied when P = 500? (1 mark)
- Graph the supply function. (1mark)
- The demand and supply functions for a good are given by:
ππ = 50 β 3ππ
ππ = 14 + 1.5ππ
- Calculate the equilibrium P and Q. (2 marks)
- Calculate ππ and ππ when P = 38. (1 mark)
- Calculate ππ and ππ when P = 20. (1 mark)
- The demand and supply functions for a good are given by:
ππ = 1620 β 20ππ
ππ = 960 + 40ππ
- Calculate the equilibrium P and Q. (2 marks)
- Graph the supply and demand functions on the same graph. (2 marks)
- Suppose the government imposes a tax of 120. Calculate the equilibrium price and quantity when the tax is imposed. (2 marks)
- Calculate the amount of tax paid by the consumer and the amount of tax paid by the producer. (2 marks)
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