Please take a look at this question. 3. Consider a monopoly in a market. It has
ID: 1131375 • Letter: P
Question
Please take a look at this question.
3. Consider a monopoly in a market. It has a constant marginal cost of 4 and a fixed cost of 4. The market demand is described by D = 50- (a) Making use of the demand function, derive the revenue and marginal revenue that the firm is facing. Show the demand, marginal revenue, and marginal cost in a simple diagram. Verify that the marginal revenue curve divides horizontally the space between the vertical axis and the demand curve equally Econ 471/po Professor Kar-yiu Wong (b) Determine the optimal output (to maximize the firm's profit) chosen by the firm Find out the corresponding market price and the profit of the firm. Also determine the consumers surplus and the welfare of the market. Show the output and market price in the diagram you constructed in (a) (c) Compute the deadweight loss associated with the monopolist. (d) If the firm acts like a competitive firm, i.e., taking the market price as given, what is the equilibrium price? (You need to make use of the demand curve rather than the marginal revenue curve.) Determine the output, market price (called the competitive price in the present case), profit of the firm, consumers surplus, welfare, and deadweight loss. Show the competitive price and output in the diagram for (a) (e) Compare your results in (b) and those in (d), and argue that the case in (d) is what the government/society wants. Why would the firm not produce the output determined in (d)? Explain why a monopolistic firm is often said to under- produce but over-chargeExplanation / Answer
Question 3). a). Solution :- Q = 50 - P (Demand equation)
P = 50 - Q (Inverse demand curve equation)
Total revenue (TR) = P * Q
= (50 - Q) * Q
= 50Q - Q2
MR = 50 - 2Q (The slope of marginal revenue curve is twice that of the slope of inverse demand curve equation or marginal revenue function is the first derivative of total revenue function.)
Conclusion :-
Question 3). b). Solution :- For calculating the optimal output, equating marginal revenue (MR) and marginal cost (MC).
50 - 2Q = 4
50 - 4 = 2Q
46 = 2Q
Q = 46 / 2
Q = 23.
P = 50 - 23 (Put the value of Q = 23 in the inverse demand curve equation i.e., P = 50 - Q)
P = $ 27.
Total revenue (TR) = 23 * 27 = $ 621.
Total cost = Total variable cost + Total fixed cost
Total cost = 4 * 23 + 4 (Fixed cost will remain $ 4 irrespective of number of units of good produced by firm.)
Total cost = 92 + 4
Total cost = $ 96.
Profit = Total revenue - Total cost.
= 621 - 96
= $ 525.
Conclusion :-
Total revenue (TR) 50Q - Q2 Marginal revenue (MR) 50 - 2Q