Well if you break the question down into its components, it's a very straightforward one to attempt.

Q: Explain Arc and Cross elasticities and analyze their role in decision making by the consumers. Point out application of these theories; quote such examples and explain. (2018)

A:
-First explain what Arc and Cross elasticities are. Give their definition, formulae and explaining graph as well along with a simple example.

-Then we are asked what role they play in a consumer's decision making. Put simply Arc Elasticity helps consumers decide on whether to buy a single product or not when a price should change (usually the change is rather large- doesnt matter whether positive or negative. When change is small point elasticity is preferred). Since Arc Elasticity measures the responsiveness of the demand with respect to price in between two points on the demand curve, it helps consumers decide whether the good is fairly elastic (i.e. change in price has drastic effects on demand) or inelastic (i.e change in price should have fairly little effect on demand).
Also note that demand curves are not straight lines- they curve away from the origin. Hence arc elasticities can also help us understand another consumer tendancy; the less the price the more eleastic the good (i.e consumers are more willing to change their consumption pattern) and the higher the price the more inelastic (i.e the consumer is less willing to change their current demand pattern or maybe they can't afford it anymore at the high prices)
Cross elasticities on the other hand help consumers decide on whether to buy a good in response to changes on related goods. E.g whether one should or should not shift to eating chicken when the prices of beef have risen and hence beef is comparatively more expensive? These kind of questions can be answered using cross elasticities which can not only tell you HOW a good is related (i.e whether it is a substitute, a complementary good or completely unrelated) but also tell you how elastic their demand and prices are to each other. It is an invaluable tool if used and understood correctly.


-the last portion of the question asks you to note down the applications of these theories with examples. Now what we wrote in the second portion above is basically the application of these two type of elasticities from a consumer perspective. Very briefly restate these with exaples and explanations (draw graphs- economists LOVEEEE graphs). Then move on to its application on the producer side. You can find that on the internet easily. Cross elasticities help not only pricing policies but also business decisions. Here is a good article to help with this https://www.businesstopia.net/econom...ecision-making
You can find similar articles for arc elasticities.


-At the end simply write a conclusion which states that these two are important concepts in economics and are powerful tools if used and understood properly.



I hope the above explanation helped. I tried not to ramble but I have a tendency to go off on tangents so feel free to ask if anything doesn't make sense. Best of luck!!