Answer to Question #218127 in Microeconomics for Pashie

Question

A monopolist is faced with two distinct damned function given as Q1=48-025P1----(1), Q2=15-0.04P2----(2).If TC=60+15Q----(3) Question. (1) Demonstrate the profit levels for market with discrimination. (2) Demonstrate the profit levels for market without discrimination.(B) Discuss your observation.

Answer 1

Solution:

1.). The profit levels for the market with discrimination:

We will have to calculate the profit maximization of the two distinct markets separately:

First derive the profit that maximizes market 1:

Demand function for market 1: Q₁ = 48 - 0.25P₁

Derive the inverse demand function:

P₁ = 192 – 4Q

Derive the total revenue:

TR = $P\times Q = (192 - 4Q)\times Q = 192Q - 4Q^{2}$

Derive Marginal Revenue (MR):

MR = $\frac{\partial TR} {\partial Q} = 192 - 8Q$

Derive Marginal Cost (MC):

TC = 60 + 15Q

MC = $\frac{\partial TC} {\partial Q} = 15$

Set MR = MC to maximize profits:

MR = MC

192 – 8Q = 15

192 – 15 = 8Q

177 = 8Q

Q = 22 units

Substitute in the demand function to derive price:

P₁ = 192 – 4Q

P₁ = 192 – 4(22) = 192 – 88 = 104

Profit level of market 1:

Profit = TR – TC

Profit = (104$\times$22) – (60 + 15(22))

Profit = 2,288 – 390 = 1,898

Profit level of market 1 = 1,898

Profit maximization for market 2:

Demand function for market 2: Q₂ = 15 - 0.04P₂

Derive the inverse demand function:

P₂ = 375 – 25Q

Derive the total revenue:

TR = P$\times$Q = (375 – 25Q) $\times$ Q = 375Q – 25Q²

Derive Marginal Revenue (MR):

MR = $\frac{\partial TR} {\partial Q} = 375 - 50Q$

Derive Marginal Cost (MC):

TC = 60 + 15Q

MC = $\frac{\partial TC} {\partial Q} = 15$

Set MR = MC to maximize profits:

MR = MC

375 – 50Q = 15

375 – 15 = 50Q

360 = 50Q

Q = 7 units

Substitute in the demand function to derive price:

P₂ = 375 – 25Q

P₂ = 375 – 4(7) = 375 – 28 = 347

Profit level of market 2:

Profit = TR – TC

Profit = (347$\times$7) – (60 + 15(7))

Profit = 2,429 – 165 = 2,264

Profit level of market 2 = 2,264

2.). Demonstrate the profit levels for the market without discrimination:

We have to derive one single price for both markets; therefore, we combine or sum up the demand functions of both markets:

Q₁ = 48 - 0.25P₁

Q₂ = 15 - 0.04P₂

Q_T = 63 – 0.29P

Derive the inverse demand function of the total demand function:

P = 217 – 3Q

Derive TR:

TR = P$\times$Q = (217 – 3Q) $\times$ Q = 217Q – 3Q²

Derive Marginal Revenue (MR):

MR = $\frac{\partial TR} {\partial Q} = 217 - 6Q$

Derive Marginal Cost (MC):

TC = 60 + 15Q

MC = $\frac{\partial TC} {\partial Q} = 15$

Set MR = MC to maximize profits:

MR = MC

217 – 6Q = 15

217 – 15 = 6Q

202 = 6Q

Q = 34 units

Substitute in the demand function to derive price:

P = 217 – 3Q

P = 217 – 3(34)

P = 217 – 102 = 115

Combined market single price = 115

Profit level of combined market:

Profit = TR – TC

Profit = (115$\times$34) – (60 + 15(34))

Profit = 3,910 – 570 = 3,340

Profit level of the combined market without price discrimination = 3,340

 

B.). The above calculations shows that the market generates more profits when there is no price discrimination compared to when there is price discrimination.