Question

2) A consumer’s demand function is Q = 60 – 2P.

a) Determine the inverse demand function.

b) Determine the inverse demand function’s vertical intercept.

c) Determine the inverse demand function’s horizontal intercept.

d) Determine the inverse demand function’s slope.

e) Determine the consumer’s marginal benefit for the 20th unit demanded.

f) Determine the consumer’s total benefit from purchasing 60 units.

g) Determine the market demand function if there are 10 consumers with the demand function Q = 60 – 2P.

Answer 1

Demand Fuction

The demand function clearly depics the relationship between the price and the quantity demanded of a particular product. It is written in a manner that quantity demanded is a function of price, that is :

Q is a fuction of P.

Inverse Demand Function

Inverse demand function is written in a manner that price is the function of quantity. which implies P is a function of Q, which is the inverse of the actual demand function.

Consumer’s demand function

Q = 60 – 2P

a) Determine the inverse demand function.

Q = 60 - 2P

Adding +2P on both sides, we have

Q + 2P = 60 - 2P + 2P

Which gives us the following equation

Q = 2P = 60

Now, subtract with -Q on both sides, we have

Q - Q + 2P = 60 - Q

Which gives us the following equation

2P = 60 - Q

Now, divide the whole equation by 2, we get

(2P = 60 - Q) / 2

P = 30 - 0.5Q

Note : Assume coefficient of Q = 1, so 1/2 = 0.5

b) Determine the inverse demand function’s vertical intercept.

In economics, the vertical axis is nothing but the Y axis that places Price (P).

Inverse Demand Function that we derived is P = 30 - 0.5Q

The price intercept of the demand curve is the point on the axis where the price is cut when the quantity demanded is a certain amount. So when the demand curve cuts the price axis the quantity demanded will be 0.

P = 30 - 0.5Q

Substitute 0 to Q

P = 30

Therefore, Co-ordinates (x,y) will be (0,30)

Demand curve based on the vertical intercepts, we know that the quantity demanded is zero when the price of the product is at $30 (P=$30)\

c) Determine the inverse demand function’s horizontal intercept.

In economics, the horizontal axis is nothing but the X axis that places Quantity (Q).

Similar to the price intercept, the horizontal intercept is nothing but the point on the axis where quantity demanded is cut when the price is a certain amount. So when the demand curve cuts the quantity demanded axis, the price will be 0.

P = 30 - 0.5Q

Substitute 0 to P

0 = 30 - 0.5Q

Taking -0.5Q to the LHS

0.5Q = 30

Q = 30/0.5

Q = 60 units

Therefore, coordinates (x,y) will be (60,0)

Demand curve based on the horizontal intercepts, we know that the quantity demanded is 60 units when the price of the product is at 0 (Q=60 units)

What we understand from this is that there is a finite demand for the product even when its priced at $0 or in other words for free

d) Determine the inverse demand function’s slope.