Answer to Question #274094 in Microeconomics for Hi3.3

Question

A profit-maximizing monopoly produces a good with constant marginal cost, MC = 20, that it sells in two countries. The inverse linear demand curve is Pi = 60 - 20, in Country 1 and P2 = 40 - ₂ in Country 2. What is the equilibrium price and quantity in each country if resale between the countries is not possible? What is the equilibrium price and quantity in each country if resale between the countries is possible? Compare the two equilibria.

Answer 1

Task #274094

Solution:

$MC =20$

To calculate the marginal revenue function:

Country 1 $MR =60-2(20Q)= 60-40Q$

Country 2 $MR= 40-2(2Q) =40-4Q$

To find the equilibrium quantity in each country, equate:

$MR=MC$

For country 1

$60-40Q =20$

$Q=1$

Equilibrium price will be found by substituting Q in the inverse demand function.

$P1=60-20(1)=40$

$P1=40$

Country 2

$MR =MC$

$40-4Q=20$

$Q=5$

Equilibrium price will be found by substituting Q in the inverse demand function.

$P2=40-2(5) = 30$

$P2=30$

Comparing the two equilibria in country 1 and country 2, the quantity demanded is less in country 1 because the price is high with a difference of 10 compared to country 2. In country 2 the units demanded are more by 4 compared to country 1 because the price is less by 10 compared to country 1.