Economist theory is - reduced prices will result in reduced profit margin, thus hurting local business.
Rundown to each option -
A. A recent survey by one of the most prominent trade magazines has suggested that a few other countries are also planning to cut down their timber prices in the international market.
Even if other countries are going to do this, local businesses will still get hurt.
B. Targania’s new export price is above the minimum price limit of export timber imposed by the International Timber Export Countries Association (ITECA), a price below which no country is allowed to export timber.
Not so relevant. Also, local businesses will still go out of business if price reductions are substantial.
C. Many neighboring countries in the timber export market have imposed similar price restrictions and seen an increase in exports.
This one is bit tricky but having an increase in export doesn't mean local businesses flourished after imposing the restrictions.
D. Local manufacturers can make up for the reduced profits by selling other products more aggressively in the local market.
Selling products aggressively in the local market may not result in the increased profit (most of the time, it does the opposite).
If option was about somehow increase in profit for local businesses in the local market, this option could had been a good choice.
E. The government uses the exports proceeds to invest in technological advancements to help the local industries to cut costs and most of such past programs have been successful.
Correct answer. As per this option, local business may not see decline in profit even after the reduction in export prices.
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Kudos are always welcome.

Economist: To increase exports, the government of Targania has planned to reduce the price at which it exports timber and has, therefore, reduced the price at which it buys timber from local manufacturers. Even though sales will increase, the plan, because of the lower profit margins, will lead to a decline in profits for timber manufacturers, forcing some of them into losses. Therefore, in the interest of the local manufacturers, the government should shelve the plan to increase the exports.

What i understand: So country T -> In order to increase the exports , it brings down the price of timber. Ok, so to keep themselves far from loses, it cuts down the price it pays the manufacturers.
So, Manufacturers will no longer get their past profits. If this continues, even though exports shoot up few manufactures will get lower profits or few might bit the dust.
We should weaken the author's suggestion of dropping the idea of "government's plan to increase the exports"

To weaken we should give a solid reason that would felicitate the continuity of the government's plan.

Which of the following, if true, casts the most doubt on the economist’s recommendation?

A
A recent survey by one of the most prominent trade magazines has suggested that a few other countries are also planning to cut down their timber prices in the international market.

Ok..other countries do follow the same plan, but how would it help us to with the aspect of country T. Probably in that country the entire timber is under government control. There are no private owners. What if the other country's timber quality is inferior and not preferred by consumers?

B
Targania’s new export price is above the minimum price limit of export timber imposed by the International Timber Export Countries Association (ITECA), a price below which no country is allowed to export timber.

Not at all effective in addressing our concern. Even though the price cut on the timber manufacturers is ethical, they still suffer.

C
Many neighboring countries in the timber export market have imposed similar price restrictions and seen an increase in exports.

Same as A. Doesnt answer our problem.

D
Local manufacturers can make up for the reduced profits by selling other products more aggressively in the local market.

"OTHER" products -> classic out of scope answer.

E
The government uses the exports proceeds to invest in technological advancements to help the local industries to cut costs and most of such past programs have been successful.

It means that government is always helpful in paying back the profits for the economic uplift of industries. Hence the industries even lose their piece of profits in the timber sale, they can get aid from government to bring down their costs involved. WOW! this is convincing and hence we can say that the proposed PLAN should continue!
E is hence the true weakener