Question

In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices PnPy and final prices p , For each problem, you are to find: (a) the oltinnal eholCY? at the ini.ial prí军戦 (b) the optimal choice at the final prices (c) the change optimal choice at final prices-optimal choice at initial prices (d) the income effect and the substitution effect

Textbook: Nicholson & Snyder, Microeconomic Theory, 12th edition.

Answer 1

(d) Income effect: with increase in income there is decline in purchase of x, dx/dI<0.It is of perverse nature for inferior goods.

p x  A
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B Gives Total effect on x *.A
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C gives Substitution effect dx/dp<0,C
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B gives income effect dx/dI<0.Here decrease in px causes increase in x but here substitution effect is larger enough to neutralise the perverse income effect.

Substitution effect:It is always opposite to the price movement. Income effect is opposite the price movement for a normal good and directly proportionate to the the price movement for an inferior good.

(a) In order to calculate MRS, we first calculate Marginal Utilities Then we calculate MRS as: x y α α − = 1 Since MRS equals the slope of the budget line, we get: Consumer Choice We will use x* and y* to represent our solution Solving for y*: * 1 * x p p y y x α −α = Since all money is spent, we also have: pxx* + pyy* = m So: * 1 * x p p p x p y x x y α −α + m p xx = = α * * 1 * p x p x x x α −α = + y x p p x y = − * * 1 α α (cont 2) m p xx = α * If Then x p m x α = * Gives ( ) y p m y −α = * 1 Finally: So, our solution is: px m x α = * ( ) y p m y −α = * 1 Substituting this into * 1 * x p p y y x α −α = (from before)

(b)The two methods for finding the optimal choice – MRS = p1 / p2 – Maximizing the Utility function •

If Then x p m x α = * Gives ( ) y p m y −α = * 1 Finally: So, our solution is: px m x α = * ( ) y p m y −α = * 1 Substituting this into * 1 * x p p y y x α −α = (from before)

c) Generally all money is spent • That is p1x1* + p2x2* = m • We find savings by considering consumption choices.