Question

1. Suppose a firm faces the following demand for its output q: q = 100 – 10p, where p represents the price it receives per unit sold. Assume this firm marginal cost is MC = 4. The level of output at which this firm maximizes its profit is______ . (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed.) The price charged at this firm’s profit maximizing level of output is __________.

2. Suppose a firm faces the following demand for its output q: q = 100 – 10p, where p represents the price it receives per unit sold. Assume this firm marginal cost is MC = 4. The absolute value of the price elasticity of demand at this firm’s profit maximizing level of output is _________. The markup over marginal cost, or Lerner Index, at this firm’s profit maximizing level of output is ___________ percent. (NOTE: write your answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading zero when needed. )

Answer 1

1.

Demand for its output q: q = 100 – 10p

Inverse demand curve: p= (100-q)/10

Total revenue(TR)= p x q= (100q-q² )/10

Marginal revenue(MR)= Differentiation of TR with respect to q= (100-2q)/10

MC= 4

Profit Maximizing condition:

MC= MR

4 = (100-2q)/10

40 = 100-2q

2q = 100-40

q = 60/2= 30 Profit maximizing output

Use q= 30 in demand function:

p = (100-30)/10= 70/10= 7 Profit maximizing Price

2.

q= 100-10p

Price elasticity of demand= (dq/dp) x q/p

Where, dq/dp= Differentiation of q with respect to p

q= Profit maximizing quantity= 30

p= Profit maximizing price= 7

q= 100-10p

dq/dp= -10

Price elasticity of demand= -10 x 7/30= -(2.33)

The absolute value of Price elasticity of demand is 2.33

Learner's index: (p-MC)/p = -1/Price elasticity of demand

p= 7

MC= 4

Markup over marginal cost= (7-4)/7 x 100= 42.86 %