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Derive the marginal rate of substitution

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Reference no: EM132559555

Consider a situation where a consumer demands two goods, x and z with the utility function U¯ = x 0.4 z 0.6

(a) Derive the marginal rate of substitution.

(b) Derive the demand functions for x and z as a function of income (Y ), the price of good x, (px) and the price of good z (pz).

(c) Let Y = 100, px = 8, and pz = 5. Find the equilibrium quantities demanded for this consumer.

(d) Now, let's say that good x gets half as expensive, p' x = 4 , but nothing else changes. Find the new equilibrium quantities demanded for this consumer.

(e) Calculate the decomposition bundle.

(f) Calculate the total, income, and substitution effects for good x.

(g) Now if the utility function is U = 10 + x 0.4 z 0.6 instead of what was described earlier, the answers you found would not change. Give an intuitive reason why the answers would not change. [Hint: note that the MRS does not change.]

Reference no: EM132559555

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