Answer to Question #158100 in Microeconomics for Abdul Mannan

Question

Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions:

Bangladesh Q1 = 12 – P1

Sri Lanka Q2 =  8 – P2

Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is

C = 5 + 2 (Q1+ Q2)

      a. Determine the company’s total profit function. Also,

(i) What are the profit maximizing levels of price and output for the two markets?

(ii) Calculate the marginal revenues in each market.

      b. Now consider two cases:

(i) Company is effectively able to price discriminate in thetwo markets. What will 

       be the total profits?

(ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit maximizing levels of price,output, and the total profits?

c. Analyze, with graphs, the two alternative pricing strategies available to the company. 

Answer 1

Answer:

Step 1

a) The formula of the total profit of the company is:

Total profit= total revenue of Bangladesh + total revenue of Sri Lanka- total cost

The calculation of total revenue of Bangladesh and Sri Lanka is:

Total revenue of Bangladesh = price x quantity

= (12-Q1) x Q1

= 12Q1 - Q1²

Total revenue of Sri Lanka = price x quantity

                                                   = (8-Q2) x Q2

                                                   = 8Q2 - Q2²

The calculation of total profit of the company is:

Total profit= total revenue of Bangladesh + total revenue of Sri Lanka- total cost 

= (12Q1 - Q1² +8Q2 - Q2²)- [5+2(Q1 +Q2)]

= (12Q1 - Q1² +8Q2 - Q2²)- (5+2Q1+2Q2)

= 12Q1 - Q1² +8Q2 - Q2²- 5-2Q1-2Q2)

= 10Q1 + 6Q2-Q1²-Q2²-5

Step 2

i) The profit will be maximized when the marginal cost (MC) is equal to marginal revenue (MR) of price and output for two markets.

ii)The marginal revenue is the derivative of the total revenue function. Therefore, the marginal revenue of the company for both the markets is:

marginal revenue of Bangladesh = $d \over dQ$(total revenue of Bangladesh)

= $d \over dQ$(12Q1 - Q1²)

= 12-2Q1

marginal revenue of Sri Lanka = $d \over dQ$(total revenue of Sri Lanka)

                                                          = $d \over dQ$(8Q2 - Q2²)

  = 8-2Q2

b)

Step 1

Price discrimination is a practice wherein the seller is able to charge a different price for different consumers. In order to be able to price discriminate, the seller must possess some order of monopoly power.

Step 2

b (i). If the company is able to price discriminate, it will sell at the profit maximizing price and quantity at both markets. This basically means that the company will charge different prices for different markets.

 

First, the profit maximizing levels of output and price is calculated for both markets.

For country B

P=12-Q

C=5+ 2Q

TR= (12-Q)Q

TR = 12Q-Q²

MR= $dTR \over dQ$= $d(12Q-Q^2) \over dQ$

MR = 12-2Q

TC = 5+2Q

MC= $d TC \over dQ$= $d(5+2Q) \over dQ$

MC= 2

MR= MC

12-2Q= 2

10= 2Q

Q= 5

P= 12-5

P= 7

Now calculate the same for country S,

P=8-Q

C=5+ 2Q

TR= (8-Q)Q

TR = 8Q-Q²

MR= $dTR \over dQ$= $d(8Q-Q^2) \over dQ$

MR = 8-2Q

TC = 5+2Q

TC= $d TC \over dQ$= $d(5+2Q) \over dQ$

MC= 2

MC= MR

2=8-2Q

2Q= 6

Q= 3

P= 8-Q

P= 8-3

P= 5

Using the calculated values, calculate the total profit for the company.

π=(TR₁+TR₂)−TC

π=(12Q₁−Q₁²)+(8Q₂−Q₂)−5+2(Q₁+Q₂)

π=(12(10)−(10)²)+(8(3)−(3)²)−(5+2(10+3))

π=20+13−31

π=2 Pak Rs

ii) without price discrimination, the profit will be calculated in the below given manner.

Q=Q₁+Q₂

Q=20−2P

P=10- $Q \over 2$

C=5+2Q

TR = (10- $Q \over 2$)Q

TR= 10Q- $Q^2 \over 2$

MR= $dTR \over dQ$= $d{(10Q- Q^2) \over 2} \over dQ$

MR= 10-Q

MC= $d TC \over dQ$= $d(5+4Q) \over dQ$

MC = 2

MR=MC

10-Q=2

Q=8

P=10-$Q \over 2$

P=10-$8 \over 2$

P= 6

π=TR-TC

π= (10(8)-$8^2 \over2$)-5+4(8))

π= 48-37

π= 11

Thus the profit is 11 Pak Rs.

c) the graphs for price discrimination and no price discrimination are given below

1. No price discrimination graph

With Price discrimination

Here the red line belongs to the Country B and blue line belongs to country S.