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The consumer is choosing between two goods- good1 and good2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods.

1. Let the utility function of the consumer be U (X1, X2) = X1(1/2)X2(1/2).

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

2.Let the utility function of the consumer be U (X1, X2) = X1(1/4)X2(3/4).

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

3. Let the utility function of the consumer be U (X1, X2) = X1+X2.

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

4. Let the utility function of the consumer be U (X1, X2) = 2X1+3X2.

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

5. Let the utility function of the consumer be U (X1, X2) = Min (X1, X2)

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

6. Let the utility function of the consumer be U (X1, X2) = 2X1 + X22.

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

7.Let the utility function of the consumer be U (X1, X2) = X1*X2

a) Calculate the Marginal rate of substitution.

b) Calculate the optimal consumption bundles.

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Darryn D'Souza
Darryn D'SouzaLv10
30 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)

Harry Mazzola has the utility function u(x1, x2) = min{x1 + 2x2, 2x1 + x2}, where x1 is his consumption of corn chips and x2 is his consumption of french fries.

(a) At the point where Harry is consuming 5 units of corn chips and 2 units of french fries, how many units of corn chips would he be willing to trade for one unit of french fries?

Suppose that there are two goods (X and Y). The price of X is $2 per unitu, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8Y^.2

Consumer A has an income of $100, and Consumer B has an income of $300.

1. Derive the marginal utlities of goods X and Y for consumer A


2. Derive the marginal utilities of goods X and Y for consumer B


3. Set consumer A's MRS equal to the price ratio. Then use the budget constraint to solve for her optimal bundle


4. Set consumer B's MRS equal to the price ratio. Then use the budget contraint to solve for his optimal consumption bundle.


5. Calculate the MRS for each consumer at their optimal consumption bundles.


6. Suppose that there is another conusmer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's MRS at her optimal consumption bundle? Why?


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