Suppose that fixed costs for a firm in the automobile industry (start-up costs of factories, capital equipment, and so on) are $5 billion and that variable costs are equal to $17,000 per finished automobile. Because more firms increase competition in the market, the market price falls as more firms enter an automobile market, or specifically P = 17,000 + (150/n), where n represents the number of firms in a market. Assume that the initial size of the U. S, and the European automobile markets are 300 million and 533 million people, respectively. a. Calculate the equilibrium number of firms in the U. S. and European automobile markets without trade.
b. What is the equilibrium price of automobiles in the United States and Europe if the automobile industry is closed to foreign trade?
c. Now suppose that the United States decides on free trade in automobiles with Europe. The trade agreement with the Europeans adds 533 million consumers to the automobile market, in addition to the 300 million in the United States. How many automobile firms will there be in the United States and in Europe combined? What will be the new equilibrium price of automobiles?
d. Why are prices in the United States different in (c) than in (b)? Are consumers better off with free trade? In what ways?

Explanation:

Given that:

where;

P = the price and;

n is the number of firms.

Now, Recall that:

where:

AC = average cost

F = fixed cost

Q = output of firm C

C = variable cost (The marginal cost is determined by variable costs and is influenced by fixed costs.)

S = The automobile sector's demand in each nation

But since avg. cost per unit, as well as the price, are just the same;

Then;

AC= P

So, S is now worth $300 million in the United States.

Then, we get the value of n for the United States by replacing the values of S, F, and C in equation (1).

By solving:

n = 3

Similarly, S is valued at $53 million in Europe.

We get the estimated value of n for Europe by replacing the necessary values in equation (1).

Thus, by solving:

n = 4

Hence;

In the United States, the equilibrium number of companies is 3.

In Europe, the equilibrium number of firms is 4.

B)

Replacing the values for n in the equation:

we can determine the value of P in the United State:

= $17050.

Similarly, replacing the value for n in the equation;

we  can determine the value of P in Europe

i.e.

= $17037.50

C)

S is worth $833 million in the United States and Europe combined.

i.e (300 million + 533 million).

Replacing the values for S, F, and C in equation (1);

By solving;

The estimated value of n for both the United States and Europe is n = 5

However, replacing the value for n in the equation below, we have:

= $17030

Thus, the new equilibrium price of automobiles = $17030

D) Automobile prices have dropped to $17,030 per vehicle for both countries as a result of free trade. As a result, after the exchange is opened, customers would have to pay a reduced amount for an automobile purchase. Not only that but after the exchange, customers in each country have a wider range of products to choose from.

The amount of brands in the United States has increased from three to five, while in Europe it has increased from four to five. As a result, trade benefits customers in both countries.