Question

The monthly demand q for a monopolist firm's product in a certain market (measured in 1000s of units) is related to the price per unit of their product, p (measured in dollars) and the average monthly disposable income in the market, yd (measured in $1000s) by the equation q = 20 ln(7yd - 2p).
When the firm's price is $4 and the average income in the market is $3000, the marginal demand, ∂ q/∂ p, for the firm's product is approximately:

a) -6.25 b) -3.08 c) -4.17 d) -1.76

Answer 1

Answer: (b) -3.08

Explanation:

The relationship between the demand(q), price per unit product(p) and the disposable income,yd is given by the expression below;

q= 20ln(7yd-2p).

From the expression above, the marginal demand,

∂ q/∂ p is the differential of the equation of relationship between the demand, price and disposable income.

This involves considering the demand,q as the dependent variable and the price per unit product,p as the independent variable and the disposable income,yd is considered constant.

Therefore ,

∂ q/∂ p= (-40)÷(7yd-2p)

By substitution of

yd =$3000÷1000= $3

and p= $4

∂ q/∂ p= (-40)÷((7×$3)-(2×$4))

∂ q/∂ p= -40÷13= 3.08

Please see the attachment for knowledge on how ∂ q/∂ p was obtained.