Question

# Consider a monopolist facing a market demand given by p=100-2q Where p is the price and...

Consider a monopolist facing a market demand given by p=100-2q
Where p is the price and q is the quantity, the monopolist produces good according to the cost function c(q)=q^2 +10
A determine the profit-maximizing quantity and the price the monopolist will offer in the market
B calculate the profits for the monopolist

C calculate the deadweight loss due to a monopoly. Illustrate this in a well-labelled diagram.

Ans. Demand function, p = 100 - 2q

=> Total Revenue, TR = p*q = 100q - 2q^2

and marginal revenue, MR = dTR/dq = 100 - 4q

Cost function, C = q^2 + 10

=> Marginal cost, MC = dc/dq = 2q

a) At profit maximizing level,

MR = MC

=> 100 - 4q = 2q

=> q = 16.67 units

At this quantity, price from the demand function,

p = 100 - 2*16.67 = \$66.67

b) Profit = TR - C = 1111.11 - 287.77 = \$823.33

We need to calculate q when p = MC,

=> 100 - 2q = 2q

=> q' = 25 units and MC = p' = \$50

Deadweight loss = area of the shaded triangle = 0.5*(p - p') *(q' - q) = 0.5*(66.67 - 50)*(25 - 16.67) = \$69.4305

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