From the point of view of the consumer, an indirect tax can be seen as an increase in the price of a certain good. This implies that the effect of the tax will depend on the behaviour of the consumer and on the importance given to the good being taxed.
This will, therefore, affect the budget constraint of the consumer, as the price of one good is higher.
Given this increase of the price, if the good being taxed is an ordinary good, the consumer will decrease the its quantity demanded.
Consequently, the revenue from the tax is directly related to the reaction of the consumer. If the tax is too high, and if it is possible to substitute the good being taxed for another one, the consumer has the choice to stop consuming it and therefore the revenue will be zero or close to zero.
So the tax needs to be fixed in a way that even with a decrease in the consumption, it will still be possible to collect revenue.
The direct tax has different implications; one good example is the income tax, which affects directly the income of the consumer. Hence, the revenue of the tax will not be directly affected by the behaviour of the consumer, but it can have indirect consequences. By seeing his income decrease, the consumer may choose to reduce generalized consumption, which might lead to negative effects to the government, mitigating the revenue collected before.
For these reasons, the tax needs to be applied in a way that does not lead to unintended negative effects from the behaviour of the consumer.
In a different matter, and assuming that the tax is well implemented and that the revenue from both types of taxes is equal, which of them is preferable to the consumers? Which will lead to a higher utility?
From the picture below, we can see that the direct tax (point C) will lead to a higher utility when compared to the indirect tax (point B) .
The blue is the initial budget constraint, which will be moved to the red line with the imposition of the indirect tax, and shifting the optimal point from A to B. If the tax being imposed is the income tax, the blue line will move downwards to the green one, and the optimal price is now C.
As IC2 is higher than IC1, the consumer is better off with the application of the direct tax.
However, the income tax has also the underline objective of redistribution, and therefore, the Government must take into account not only efficiency but also equity.
In order to apply a decent tax structure, it is necessary to keep in mind several conditions in order to attain the results intended. This means that it is essential to understand what the consumers prefer, which as seen above is the income tax because it leads to higher utility. Moreover, bear in mind that the goal of the Government is also extremely important. Meaning that if it is only looking for efficiency, maybe the direct tax is better, though if it is considering the importance of redistribution it needs to apply an income tax.