A monopolist's demand fQuestion 1.
unction is given as Y=2000-10K, where Y is the quantity of output produced and sold and K is the price per unit in Tshs. If the marginal cost is Tshs 100
Calculate the monopolist's equilibrium quantity and price.
Suppose the Monopolist behaves competitively, how would the answers in a) above change?
Show the inefficiency caused by the above monopolist diagrammatically and mathematically.
To find the monopolist's equilibrium quantity and price, we need to determine the point where the monopolist's marginal cost (MC) equals the marginal revenue (MR).
Step 1: Calculate the monopolist's marginal revenue (MR) curve:
The monopolist's marginal revenue is given by the derivative of the demand function. So, taking the derivative of Y = 2000 - 10K with respect to K, we get MR = 2000 - 20K.
Step 2: Set MR = MC and solve for K:
2000 - 20K = 100 (since marginal cost is 100)
Solving this equation, we find K = 95.
Step 3: Substitute the value of K into the demand function to find the equilibrium quantity:
Y = 2000 - 10K
Y = 2000 - 10(95)
Y = 2000 - 950
Y = 1050.
Therefore, the monopolist's equilibrium quantity is 1050 units and the equilibrium price is Tshs 95.
Now, let's consider how the answers would change if the monopolist behaved competitively.
In a competitive market, firms are price takers and do not have control over the market price. They have to accept the market price as given. So, the monopolist's equilibrium price would change to the competitive market price, which would be determined by the intersection of the industry's supply and demand curves.
Assuming perfect competition, the market price would equal the marginal cost (MC) of production since firms produce where MC equals the market price. So, the equilibrium price would be Tshs 100.
The equilibrium quantity would depend on the demand curve of the entire market, and it cannot be determined without more information.
Moving on to the inefficiency caused by the monopolist, we can illustrate it both diagrammatically and mathematically.
Diagrammatically:
In a monopoly, the equilibrium quantity is lower and the equilibrium price is higher compared to a competitive market. This is because the monopolist restricts output to increase prices and maximize its profits. The inefficiency is shown by the deadweight loss, which represents the foregone social surplus due to the monopolist's market power.
Mathematically:
The inefficiency caused by the monopolist can be measured by comparing the social surplus in a monopoly to the social surplus in a perfectly competitive market.
Mathematically, social surplus is the sum of consumer surplus and producer surplus. In a perfectly competitive market, social surplus is maximized because the market price is equal to the marginal cost of production.
The inefficiency caused by the monopolist is represented by the difference between the social surplus in a monopoly and the social surplus in a perfectly competitive market. This difference is equal to the deadweight loss.
Calculating the deadweight loss requires knowing the demand and supply curves, which are not given in this question.