Question

Suppose your firm is told that the demand function it faces from its market is given by

Q = 8 − 0.5p

Its cost per unit is constant and equal to $1.5. Assume that it produces integer number of units (i.e. Q = 0,1,2, 3…and so on).

1. Describe in how you would use this demand function above to obtain your consumers’ marginal utility (or maximum willingness-to-pay) for each unit of your firm’s product.

Answer 1

Demand Function :

Q = 8 - 0.5P

Now we find the inverse demand function in terms of Quantity, which would give us the price for each level of quantity.

Inverse demand function:

0.5P = 8 - Q

P = 8/0.5 - Q/0.5

P = 16 - 2Q ..... eq(1)

The eq(1) is the inverse demand function which gives the price a consumer is willing to pay for each quantity.

(i) Let us suppose quantity = 1 unit. So substituting Q = 1 in eq (1) gives,

P = 16 - 2(1)

P = 16 - 2

P = 14

(ii) Let Q = 2

P = 16 - 2(2)

P = 12

The value of 'P denotes the maximum willingness to pay of a consumer for each quantity level.

We can see that as the quantity increases from 1 to 2 units, the maximum willingness to pay of an individual decreases from 14 to 12 (i.e. by 2 units).This happens because the coefficient of variable - quantity is equal to -2 which means that as the quantity increases by a unit, the willingnes to pay of a consumer decreases by 2 units.