Microeconomics 3 Tiffanys utility function is given by the f

Microeconomics

3. Tiffany’s utility function is given by the formula U(x1, x2) = min{2x1, 800x2}. If x1 = x2, which commodity will have a greater marginal utility?

a. x1

b. It is not possible to determine which commodity has higher marginal utility

c. Both x1 and x2 have the same marginal utility

d. x2

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_6. What is the slope of the level curves of the function f(x,y)=5x²y³?

a. -(2y)/(3x)

b. -10xy³

^c. - 1/(15x²y²)

d. -(3x)/(2y)

e. -(2y²)/(3x²)

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7. For U(x₁,x₂) = 6x₁^1/3 + x₂, preferences are

a. consistent with increasing marginal rate of substitution.

b. consistent with constant marginal rate of substitution

c. not consistent with a utility function.

d. consistent with diminishing marginal rate of substitution.

Solution

3) The correct option is C

In the utility function U(x1, x2) = min{2x1, 800x2} , X₁ & X₂ are complementary goods , therefore an increase in the consumption of X₁ causes an increase in the consumption of X₂ . It means an additional quantity of one without increase in the quantity of the other does not yield additional satisfaction .

6) f(x,y)=5x²y³

f¹(x) = 10xy³

f¹(y) = 5X² 3y²

Slope = f¹(x) / f¹(y)

slope =  10xy³ / 5X² 3y²

slope = -(2y/3x)

7) The correct option is b

explanation : The utility function represents substitute goods where the number of units of goods X₂ must be given up , to have more units of X₁ and thereby the total utility of the consumer remains the same by consuming more of goods X1 .