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Question 1

A utility function is given by u(x1, x2) = min{x1 + 2x2, 3x1 + x2}.

(a) Graphically determine the optimal consumption for the following prices and income: p1 =1, p2 =1,I =30.

(b) Suppose the price of good 2 increases to p2 = 3. Determine graphically the change in consumption of goods 2 and 3. p1 = 1, p2 = 2, I = 20.

(c) Determine the least costly consumption bundle which gives the consumer the same utility as in (b) when prices are p1 = 1, p2 = 1, i.e.

Determine the Hicksean demand.

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Romarie Khazandra Marijuan
Romarie Khazandra MarijuanLv10
28 Sep 2019

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Related questions

Currently, the price of consuming housing x1 is lowered by the fact that home mortgage interest is tax deductible. Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from (p1-s) to p1. At the same time, the government lowers the tax on other consumption x2, lowering the price from (p2 + t) to p2.

a) Write down your original budget constraint assuming the consumer has income I.

b) Suppose the utility function u(x1, x2) = (1/3) lnx1 +lnx2 captures your tastes, and suppose I = 10, 000,

p1 = 10, p2 = 1, s = 6, and t = 1. Write out the utility maximization problem for this consumer

prior to any policy change.
c) How much housing and other goods will this consumer consume prior to any policy change? (show process)

d) When the policy change goes into effect, will this consumer still be able to afford the bundle you derived in (c)?

e) When the policy change goes into effect, what bundle will the consumer consume?

Consider a consumer with utility function given by u(x1, x2) = x1x2.

(i) Find the demand for goods 1 and 2 when the consumer faces prices p1 and p2, and income m.

(ii) Are goods 1 and 2 normal goods? Why?

(iii) Are goods 1 and 2 ordinary goods? Why?

An Individual consumes good X1 and X2. Let W be the wealth of the individual and P1>0, P2>0 be the prices of the goods. For each of the utility functions provide a real life example of two goods X1 and X2 that satisfy them, draw the indifference curves, determine whether preferences are convex, strictly convex or neither, and compute the Walrasian demand, indirect utility function, Hicksian demand, and Expenditure function.

  1. U (X1, X2) =(X1^0.4) *(X^0.6)
  2. U (X1, X2) =min (X1, X2) +3 max (X1, X2)

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