Suppose the observed annual quantity of steel exchanged in the European market is 30 million metric tons, and the observed market price is 90 euros per ton. If the price elasticity of demand for steel is - 0.3 in Europe, what is an appropriate value for the price coefficient (b) in a linear demand function Q

-0.10

Explanation:

To calculate this, we us the formula for calculating elasticity of demand (E) relevant for the demand equation as follow:

E = (P / Q) * (dQ / dP) ... (1)

Where,

Q = 30

P = 90

E = - 0.3

dQ / dP = b = ?

We then substitute all the value into equation (1) and have:

-0.3 = (90 / 30) * b

-0.3 = 3 * b

b = - 0.3 / 3

b = - 0.10

Therefore, appropriate value for the price coefficient (b) in a linear demand function Q is - 0.10.

NB:

Although this not part of the question, but note that how the linear demand function will look can be obtained by first solving for the constant term (a) as follows:

Q = a - 0.10P

Substituting for Q and P, we can solve for a as follows:

30 = a - (0.1 * 90)

30 = a - 9

a = 30 + 9 = 39

Therefore, the linear demand equation can be stated as follows:

Q = 39 - 0.1P