Daenerys has an income of $100 to spend on apples (good z) and bananas (good y). Her utility function…

Daenerys has an income of $100 to spend on apples (good z) and bananas (good y). Her utility function…

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Daenerys has an income of $100 to spend on apples (good z) and bananas (good y). Her
utility function is given as
u(z. y) = 2007
The price of apples is $2, and the price of bananas is $1.
(a) Write down Daenerys’ utility maximization problem.
(b) Find the marginal utility of apples.
(c) Find the marginal utility of the bananas.
(d) Find the marginal rate of substitution.
(e) Draw the graph of Daenerys’ budget constraint and indifference curves.
(f) Find the optimal bundle (r. y) and denote it on the graph in part (e)
Suppose that the price of apples decreases to $1. We want to decompose the price
effects on apples into substitution effects and income effects.
(g) Write down Daenerys’ new budget constraints on the graph in part (e)
(h) Find the optimal bundle (a”, y”) and denote it on the graph in part (e)
(i) Let m’ be the amount of money income that will just make the bundle (r, y) from
part (f) affordable. Find the value of m’.
(j) Find the optimal bundle (z.) under pp, 1 and m’
(k) Compute the substitution effects of apples; r’ -r
(1) Compute the income effects of apples; z-r’

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This is a multi step question that involves understanding the utility function budget constraints calculating the marginal utilities the marginal rate
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