Suppose a monopolist has two segmented markets, domestic (1) and foreign (2). Th

Question

Suppose a monopolist has two segmented markets, domestic (1) and foreign (2). The demand functions for both markets and the total cost function are as follows: Find the output the firm would produce and sell In each market in order to maximize profit. What price will the firm charge in each market? Explain, with quantitative evidence, the relevance of price elasticity of demand in the determination of the relative prices charged in each market. Explain why a firm needs thorough knowledge of ATC, AVC and MC. Indicate the key market decision(s) associated with each variable. Explain the basic features of the various market structures discussed in class. What is product differentiation? How is it that in a perfectly competitive market long run economic profit is zero?

Explanation / Answer

Q1 (a) Demand function of domestic market –

P1 = 100 – Q1

Demand function of foreign market –

P2 = 80 – 2Q2

Total cost function –

TC = Q12 + 2Q1Q2 + Q22

Calculating Total revenue of domestic market –

TR = P1 * Q1 = (100 – Q1)*Q1 = 100Q1 - Q12

Calculate Marginal revenue of domestic market –

MR = dTR/dQ1 = d(100Q1 - Q12)/d Q1 = 100 – 2Q1

                        

Calculating Marginal cost of domestic market –

MC = dTC/dQ1 = d(Q12 + 2Q1Q2 + Q22)/dQ1 = 2Q1 + 2Q2

Equating MR and MC to ascertain profit-maximizing output in domestic market –

100 – 2Q1 = 2Q1 + 2Q2

4Q1 + 2Q2 = 100 or,

2Q1 + Q2 = 50    ------ equation (i)

Calculating Total revenue of foreign market –

TR = P2 * Q2 = (80 – 2Q2)*Q2 = 80Q2 - 2Q22

Calculate Marginal revenue of foreign market –

MR = dTR/dQ2 = d(80Q2 - 2Q22)/d Q2 = 80 – 4Q2

Calculating Marginal cost of foreign market –

MC = dTC/dQ2 = d(Q12 + 2Q1Q2 + Q22)/dQ2 = 2Q1 + 2Q2

Equating MR and MC to ascertain profit-maximizing output in foreign market –

80 – 4Q2 = 2Q1 + 2Q2

2Q1 + 6Q2 = 80 or,

Q1 + 3Q2 = 40    ------ equation (ii)

Solving equation (i) and (ii),

We get,

Q1 = 22

Q2 = 6

Calculating price in domestic market –

P1 = 100 – Q1 = 100 – 22 = $78

Calculating price in foreign market –

P2 = 80 – 2Q2 = 80 – 2*6 = $68

In order to maximize profit,

Firm will sell 22 units in domestic market and will charge $78 per unit.

Firm will sell 6 units in foreign market and will charge $68 per unit.

(b) Calculating price elasticity of demand in domestic market –

Price in domestic market (P1) = $78

Quantity in domestic market (Q1) = 22

P1 = 100 – Q1

Differentiating P1 with respect to Q1 –

dP1/dQ1 = d(100 – Q1)dQ1 = -1

Price elasticity of demand = dP1/dQ1 * P1/Q1 = -1 * (78/22) = -3.54

The price elasticity of demand in domestic market is -3.54 or 3.54 (can be written without negative sign as well).

Calculating price elasticity of demand in foreign market –

Price in foreign market (P2) = $68

Quantity in foreign market (Q2) = 6

P2 = 80 – 2Q2

Differentiating P2 with respect to Q2 –

dP2/dQ2 = d(80 – 2Q2)dQ2 = -2

Price elasticity of demand = dP2/dQ2 * P2/Q2 = -2 * (68/6) = -22.67

The price elasticity of demand in foreign market is -22.67 or 22.67 (can be written without negative sign as well).

As one know that price elasticity of demand in each market plays an important role in determination of price to be charged in each respective market. More elastic the demand for a product in a particular market, lower will be the price charged in that market and vice-versa.

The value of price elasticity of demand in foreign market is greater than value of price elasticity of demand in domestic market; this implies that demand is more elastic in foreign market.

As demand is more elastic in foreign market with respect to domestic market, price charged in foreign market is lower than the price charged in domestic market.

Thus principle of more elastic the demand for a product in a particular market, lower will be the price charged in that market and vice-versa is clearly applying in the given case.

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