Question

You have two factories that produce identical products (lets say plastic forks). The plants and equipment are fully depreciated and there are no fixed costs.

As a result, your cost basis in the USA is TCusa = 3Yusa^2

your cost basis in CHINA is TCchina = Ychina^2

The demand for plastic forks is Y=80

a. With no restrictions (competitive markets exist) how many plastic forks will the USA produce? 2 Points

b. How much would China need to lower their cost to produce all of the 80 plastic forks? 1 Points

c. How much of a subsidy would the firm need to produce all 80 plastic forks in the USA, given the original TC functions? 1 Points

Edit: My feedback was expert couldn't solve it ,,, can we get another expert here?

Answer 1

a) Given that

TC_USA = 3 Y²_USA ........... (i)

and TC_China = Y²_China .............. (ii)

Also, the total demand for plastic fork is Y = 80 = Y_USA + Y_China ............ (iii)

Or, Y_USA = 80 - Y_China ........... (iv)

Substituting (iv) in (i)

TC_USA = 3 (80 - Y_China )² .......... (v)

Total Cost of producing forks, TC, is thus = TC_USA + TC_China

Substituting the values from (ii) and (v)

TC = 3 (80 - Y_China )² + Y²_China

TC = 3 (6400 + Y²_China - 160 Y_China) + Y²_China

TC = 4 Y²_China -480 Y_China + 19200........... (vi)

MC = 8 Y_China -480 .......... (vii)

for perfectly competitive firms,

demand = MC= MR

Hence, 8 Y_China -480 = 80

8 Y_China = 560

Y_China = 70..... (viii)

Substituting (viii) in (iii)

80 = Y_USA + Y_China

Y_USA = 80 - 70

Y_USA = 10

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b) To produce all the 80 forks, China will have to reduce its costs by 800

Cost of producing 80 forks = Y²_China = 80*80 = 6400

Cost of producing 70 forks = Y²_China = 70 * 70 = 4900

Difference in cost for producing 10 less forks = 6400 - 4900 = 1500

this implies that additional cost of producing 10 more costs is 1500, i.e., 150 per fork

Currently, the cost of producing 1 fork is 70, so increased cost is 80 (150-70)

China need to reduce the cost of production by 80 each,

the new TC*_China = Y²_China - 800, giving the cost of each of the 80 forks as 70.

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c) the cost of producing 10 forks in USA is 3 Y²_USA = 3 * (10)² = 300

and cost of producing 80 forks = 3 * 80 * 80 =19200

while in China, the cost of producing 10 forks = 100 and 80 forks is 6400

the difference is the subsidy requirement for USA = 19200 - 6400 = 12800

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