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Assume that in country A's automobile industry the start-up costs (fixed costs) for a manufacturer are $1
Assume that in country A's automobile industry the start-up costs (fixed costs) for a manufacturer are $1.2 billion. The marginal cost of producing an automobile is $12, 000. The market price per automobile decreases with the competition, i.e., automobile price falls as more firms enter the industry. Suppose the price function is: P=12,000+300/n. n is the number of firms in the market. The size of country A's automobile market is 36 million people. (1) Compute the equilibrium number of automobile manufacturers and the price of an automobile in the market. (2 points) Now assume that automobile manufacturers in country B face the same production cost function and price function as above. But country B has a bigger market of 64 million people. The two countries decide to open up the automobile market to each other. (2) How many automobile manufactures can survive in the new equilibrium? How much does an automobile cost in country A and country B, respectively, in the new equilibrium? (3 points) (3) What inference can you make from this example?
Expert Solution
P=12000+300/n
Total Cost=Fixed Cost+ Variable Cost
Fixed Cost=$1.2billion=$1200000000
Variable Cost=12000Q
TC=1200000000+12000Q
Each firm in a monopolistic market has a demand curve:
q=S[1/n-b(P-P*)]
S is the size of the market
n is the no. of firms
P is the price charged by the firm
P* is the average price charged by other firms.
Here all firms are symmetric, P=P*
q=S/n
TC=1200000000+12000q
Average Cost=TC/q
AC=1200000000/q+12000
At equilibrium, price is equal to average cost
12000+300/n=1200000000/q+12000
300/n=1200000000/q
q=S/n
300/n=1200000000n/S
300S/1200000000=n^2
(1)S=36 million=36000000
n^2=300S/1200000000
n^2=(300*36000000)/1200000000
n^2=9
n=3
Equilibrium number of automobiles=3
Price=12000+300/n
Price=12000+300/3=$12100
(2) When two countries open up to trade, S=64Million+36Millio=100Million
S=100000000
Using the above formula,
n^2=300S/1200000000
n^2=300*100000000/1200000000
n^2=25
n=5
Equilibrium number of automobiles=5
Price=12000+300/n
Price=12000+300/5=$12060
Total Cost in A and B= 1200000000+12000(100000000/5)=$252000000000
(3) As market size increases or when two markets, prices gets lowered down and consumer benefit increases.Integration of markets also reduces the average costs of the firms.
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