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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?

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Joshua Stredder
Joshua StredderLv10
28 Sep 2019

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Related questions

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)

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?

Given: U(x1, x2) = x1x2+x1


a)

Calculate the Marshallian demand for x1 and x2

b)

Graph the demand for x1 when p2= 20 and I = 100.



For Marshallian Demand I got:


x1 = (I-P2)/3P1 and x2=((2I - 2P2)/3P2) -1


is this correct? I did the Lagrangian. How would I calculate demand for x1 if I don't know the price of x1?

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