Question

a)

You are given that the supply curve for the market is:- ?=240?−2?2−4200

What does this supply curve model predict for the maximum possible price in this market? Find the quantity, ??, for this maximum possible price. You should show your working.

Plot the curve and describe the significance of the supply curve for ?>??.

Note:



There are several software packages available online that will allow to plot the curve such as geogebra, or Desmos. They can also be used to check your maximum point.

b)

You are given that the demand curve for the market is a straight line. The price decreases by 10 for every extra unit in quantity. The market is currently in equilibrium with ?=30 units.

Explain what is meant by an equilibrium point and find the other equilibrium point.

You are an economist investigating supply and demand in a particular market.

Task 4 – Supply Curve

You are given that the supply curve for the market is:-

?=240?−2?2 −4200

What does this supply curve model predict for the maximum possible price in this market? Find the quantity, ??,

for this maximum possible price. You should show your working.

Plot the curve and describe the significance of the supply curve for ? > ??.

Note:

• There are several software packages available online that will allow to plot the curve such as geogebra, or Desmos. They can also be used to check your maximum point.

Task 5 – Equilibrium Point

You are given that the demand curve for the market is a straight line. The price decreases by 10 for every extra unit in quantity. The market is currently in equilibrium with ? = 30 units.

Explain what is meant by an equilibrium point and find the other equilibrium point.

Answer 1

p = 240q - 2q^2-4200

To maximize the price wrt to a particular quantity,

d/dq (p) = 0

or d/dq (240qm - 2qm^2-4200) = 0

or 240 - 4qm = 0

or qm = 60

Maximum price = 240 * 60 - 2*60^2 - 4200 = 3000

Let us consider 2 cases where the quantity is 61 and the quantity is 59

Quantity 61:
p = 240 * 61 - 2 * 61^2 - 4200 = 2998

Quantity = 59

p = 240 * 59 - 2*59^2 - 4200 = 2998

So if we move away 1 quantity on either side from the optimal quantity of 60, then the price reduces.

So if the supply of the material is more than 60 (the optimal quantity), the market starts flooding and as a result, producers need to lower prices to sell the product. So the price goes down. This is the significance of the supply curve for q>qm. The price is highest at a quantity of 60.

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