ž: fraction that will Adopt at next time step fraction z Adopting now Q4. If you
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ž: fraction that will Adopt at next time step fraction z Adopting now Q4. If you spend $50,000 on marketing, you can get a fraction z' of the population to Adopt the app at time O. This fraction z' is between B and C-just above B, in fact. If you spend $300,000 you can get a fraction z" of the population to Adopt at time 0 (mostly by giving the App away). This fraction z" is close to D. Your intern argues that you should spend the $300,000, as it will get you close to total adoption. If adoption settles at fraction A, your company will make $0 in revenue; at fraction B, your company will make $100,000 in revenue; at fraction C, your company will make $200,000 in revenue; and at fraction D, your company will make $500,000 in revenue. Is your intern right? If not, what should you do? In all cases, you need to subtract the cost of your campaign from the revenue. Be sure to explain your reasoning. (10 pointsExplanation / Answer
The intern is wrong.
The fractions A,B,C and D are all equilibria that is Z=g(z).
If the suggestion offered by the intern is followed and we spend $300000 by giving away the app,then we end up with z' adopting at time 0.This fraction z'' is close to but lower than D however,between C and D,g(z) is less than z.This implies that the fraction that adopts at the next time step is less than the fraction which is adopting now.
The other option is spending $50000 on marketing to end up with z' adopting at time 0.This fraction is between B and C.however,g(z) is more than z between B and C.So,the fraction which adopts at the next time time step will be greater than the fraction adopting now until we reach stable equilibrium C as, g(z)>z below C and g(z)< above C so we return to C.
Both strategies lead finally to C which generates revenue of $200000.If the intern's advice is followed,then a net loss equal to ($200000-$300000)= -$100000 is generated whereas,the other strategy leads to profit equal to ($200000-$50000) = $150000.Therefore,the other strategy should be followed.
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