Question

Suppose a technology company developed a pair of very fashionable Augmented Reality eyeglasses. The firm has a marginal cost of $700 for each pair of glasses produced. A restriction prohibits the firm from setting different prices in France and Italy. The two countries have the following inverse demands: Pfrance = 4200 - 1/3QFrance Pitaly = 5595 - 3/2Qitaly If the firm can charge different prices in each country, what would QItaly be? What price would the firm set?

Answer 1

Pitaly = 5595 - 3/2Qitaly

Take:

Pitaly= P1

Qitaly= Q1

P1 = 5595 - 3/2Q1

Marginal cost= MC=700

Firm will set price and quantity where:

Marginal revenue(MR)= MC

For MR:

Total revenue(TR)= P1 x Q1= (5595 - 3/2Q1)Q1= 5595Q1 - 3/2Q1²

MR= differentiation of TR wrt Q1= 5595-3Q1

Put MR=MC

5595-3Q1= 700

3Q1= 5595-700

Q1= 4895/3= 1631.67

Put Q1 in demand function:

P1= 5595-(3/2)Q1= 5595-(3/2)(1631.67)= 5595-2447.51= 3147.49

QItaly= 1631.67

Firm set price in Italy= 3147

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Pfrance = 4200 - 1/3QFrance

Take:

Pfrance=P2

Qfrance= Q2

P2 = 4200 - 1/3Q2

Total revenue= P2 x Q2= 4200Q2-(1/3)Q2²

MR= differentiation of total revenue= 4200-(2/3)Q2

MC= 700

For price and quantity:

Put MC=MR

700= 4200-(2/3)Q2

(2/3)Q2= 4200-700

Q2= 3500 x (3/2)= 5250

Use Q2 in demand function:

P2= 4200-(1/3)5250= 4200-1750= 2450

Pfrance=2450

Qfrance= 5250