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)**

- What is the slope? What are the intercepts?
- 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)**

- What is the slope? What is the vertical intercept?
- 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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