Question

Natalie has the only permit for selling hot cocoa at a hut overlooking Lake Louise, which can only be accessed by foot. Natalie has a monopoly on the market. The demand curve for hot cocoa at the hut is given by the function p(QD) = 30 ? 1.5QD, where p is the price expressed as a function of the cups of cocoa demanded, QD. Natalie’s marginal cost expressed as a function of the number of cups she prepares is MC(QS) = 2QS ?5.

(a) Given the information provided, determine the quantity produced and equilibrium price charged by the monopolist firm.

(b) Calculate the Lerner Index at the monopoly equilibrium price and quan- tity. Recall LI = ?1/? = (P ? MC)/P.

(c) Explain in words what is measured by the Lerner Index.

Answer 1

a) P = 30 -1.5Q

TR = 30Q -1.5Q²

MR = 30 - 3Q and we have MC = 2Q -5

equilbruim price and quantity at MR=MC
30-3Q=2Q-5

5Q = 25

Q = 5

P = 30-1.5*5

P = $22.5

so, equilbruim price is $22.5 and quantity is 5

b) lerner index = P - MC / P

lernex index = (22.5 - 2Q - 5) /22.5

lernex index = ( 22.5 - 10-5) / 22.5

lerner index = 7.5/22.5 = 0.33

lerner index = 0.33

c) from lerner index - we can say that this firm has some control over price or this firm has market power . because, when lernex index is equal to 0 which means no market power or perfectly competitive industry and as the lernex index is higher, the market power also higher.