Question

1. Use the following market demand and supply equations to answer questions a and b
Qd = 100 – P, and Qs = 10 + 2P and
ATC = 0.5Q

a) Calculate the competitive market’s profit-maximizing price, quantity, and profit
b)Now assume, the market above is a Monopolist’s market. Calculate the Monopolist’s profit-maximizing price, quantity, and profit.
c)Use one graph to show everything you calculated in part a and b of this question. When you look at the graph, how is the price, quantity, and profit of the monopolist different from the competitive market?

Answer 1

Answer on Question #71629, Economics / Microeconomics

Use the following market demand and supply equations to answer questions a and b $Q_d = 100 - P$, and $Q_s = 10 + 2P$ and ATC = 0.5Q

a) Calculate the competitive market's profit-maximizing price, quantity, and profit.

Answer:

a) If the demand function is $Q_d = 100 - P$ and the supply function is $Q_s = 10 + 2P$ set

$$100 - P = 10 + 2P$$

and solve for P

$$90 = 3P$$ $$P = 30$$

Therefore the price is 30.

To solve the quantity, substitute 30 for P in either the demand function or the supply function.

$$100 - P = 100 + 30 = 15 - 6 = 70$$ $$10 + 2P = 10 + 2(30) = 10 + 60 = 70$$

Therefore the profit maximization quantity is 70.

Then the total revenue, which is $(P \times Q)$

$$TR = 30Q$$

To find total Costs

Average Costs = Total Costs / Q

Total Costs = Average Costs × Q = 0.5Q × Q = 0.5Q²

To find to the profit

Profit = TR - TC

Profit = 30Q - 0.5Q²

Profit = 30 × 70 - 0.5 × 70²

Profit = 2100 - 2450

Profit = 350

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