Sorry this might be a bit long (and late), but here we go:

India certainly felt an impact from the Great Depression, in ways one would expect economically but the Depression also had an interesting impact on the course of Indian politics.

To start off with the economic impact, the depression severely cut India’s export economy and also hurt India’s imports. To give you a general sense, India’s exports were valued at 311 crores (3110 million rupees) in 1929/1930 but by 1932/1933 the value of exports dropped immensely to 132 crores. Imports to India similarly fell from 241 crores to 133 and domestic agricultural prices fell 44 percent between 1929 and 1931, increasing tax pressures on landlords.

This leads me into my next point, that because of the tax pressures from creditors onto landlords in the midst of the Depression, landlords and tenants in India fell into conflict. This caused a bit of a debate in India’s Congress party, as Jawaharlal Nehru supported a no-rent campaign for tenants whilst Gandhi was against it in fear that it would alienate the landlords away from Congress and into British hands. Nehru was willing to do this because he figured the landlords would be deprived of their privileges anyway as allies of the British, and if he were to go against Indian landlords it would be easier from a political angle if they were seen as allies of the British against the masses of India.

Furthermore, Gandhi’s civil disobedience campaign in 1930 was becoming difficult to manage. The Great Depression had affected a lot of Gandhi’s financial supporters who were finding it increasingly difficult to finance the campaign. On the British side of things, Lord Irwin (Governor General of India at the time) was fearing peasant revolt in the North due to the effects of the depression, and Gandhi was willing to compromise especially given the state of his current movement. This lead to the Round Table Conference(s) of 1930-1932. Gandhi gained very little at the first conference as Lord Irwin basically released some prisoners and permitted Indians to make their own salt. The peasants were not given any land back as Irwin said he could not return it because the tenants could not pay their debts or the lands were auctioned off. Nehru was enraged as he felt the peasants sacrificed so much more for so little while Gandhi was content with the symbolic gesture the conference presented for British-Indian negotiation. Gandhi then met for a second conference in 1932, where the big issue on the table was how power at the centre would be shared – The British advocated for separate electorates for certain groups (ie the untouchables) as a way to undermine Congress’ support in India. Gandhi was strictly opposed to this, and left the conference to renew his civil disobedience campaign in India. He was able to do this more easily at this point because interestingly enough, due to the Great Depression, British companies were finding direct investment less profitable and began to partner with local Indian businesses. As such many Indian businesses actually expanded and arguably strengthened Indian capitalists. This in turn allowed them to support Gandhi’s national movement. With this renewal, Gandhi advocated along with Nehru this time for the no-rent campaign, gaining peasant support. Gandhi also engaged in fasts opposing separate electorates, which won Congress the sympathy and greater support from B.R. Ambedkar and the untouchables in India. Arguably, would it not have been for the Great Depression the British might have been successful in undermining Congress support from peasants and untouchables in India.

Hopefully I’ve made it somewhat clear, in a bit of a general sense, on how the depression had not just economic effects, but set off a chain reaction of political events that would lead to even more events that I didn't get to mentioning such as the Government of India Act in 1935 and so on.

Sources:

Hermann Kulke and Dietmar Rothermund, A History of India

Dietmar Rothermund, An Economic History of India, from pre-Colonial times to 1991

Judith E. Walsh, A Brief History of India

EDIT: grammar...

With regards to Palestine, it depends on the group. The Jewish sectors of the economy, which had a huge influx of Jews entering Palestine in the mid-1930s, led to a significant urban and Jewish economic boom. Thanks to an influx of German-Jewish capital, the number of industrial firms more than doubled from 6,000 in 1930 to 14,000 in 1937. This trend of growth would continue, as the Jewish industry flourished. The Jewish economy in general began to outrank the Arab in nearly every statistic by 1943, besides in citrus cultivation, where Arabs held 145,000 dunams of land and the Jews held 141,000. But by that point Jewish industry had more industrial establishments, invested 6x as much capital in industry as non-Jewish firms, and had roughly 4x as many workers in industry as non-Jewish groups.

While the Jewish economy flourished, it was often at the cost of the Arab economy, however. Arabs, who had largely been landed peoples and cultivated that land, felt the Depression too. Arab land sales to Jews were becoming slightly more common, as Arabs felt that they had to do something to survive the rougher economic times, and did not have the boon of a capital influx or new immigrants to take up labor in industry. In the public works sector, Arabs and Jews worked at a 50-50 ratio for the British, the Jewish Agency having convinced the British to employ them both equally since Jews paid 50% of the tax revenue. Given that the population distribution was around 70-30, this meant higher rates of Arabs were unable to access that sector too. Since over 90% of Arabs/Muslims lived off the land, and since the area of Palestine (as a colonial-ish entity) was a place that many other countries dumped their surplus agricultural goods, the Arab economy took a major hit during the Depression. Increasing imports meant the cost of wheat and production thereof went down dramatically, and peasants went further into debt as moneylenders began to demand money rather than wheat for payment. This contributed to a growing landless peasant class of Arab workers, who would form the backbone of the Arab Revolt that began in 1936.

When the Depression hit, Jewish groups did take a blow, and the Arab economy did overall do better until 1935 in unprecedented levels. But with the Depression came, and sanctions were placed on Italy by the League of Nations, the rush on the banks and closure of firms led to the Jewish economy trying to seize more of the jobs to limit unemployment, and a drought in 1931-1934 that had led to dropped agricultural production meant that Arabs working in industry were suddenly competing with Jewish labor in greater numbers than before, and they typically lost out, meaning they were left without agriculture or industry.