Reference no: EM13105427
Part-1
Assume preferences can be represented by the following utility function:
u(x1, x2) = 3 ln (x1) + ln (x2)
a. Is the utility function monotonic? Justify.
b. How can this person be better off than by consuming the bundle (x1, x2) = (10,10)?
c. Set up the utility maximization problem for the consumer, when facing prices p1 = 6, p2 = 2 and income m = 32.
d. Solve the problem by finding (x1*, x2*).
e. Graph the budget set, a couple of indifference curves and the optimal choice.
Part-2
Assume preferences can be represented by the following utility function:
u(x1, x2) = -x12 + 150x1 - 2x22 + 100x2 + x1x2
a. Is the utility function monotonic? Justify.
b. How can this person be better off than by consuming the bundle (x1, x2) = (100,100)?
a Set up the utility maximization problem for the consumer, when facing:
prices p1 = 2, p2 = 1 and income m = 30.
d. Solve the problem by finding (x1*, x2*).
Part-3
Assume preferences can be represented by the following utility function:
u(x1, x2) = 4ln (x1) + x2
a. Is the utility function monotonic? Justify.
b. Set up the consumer's utility maximization problem for prices pi, p2 and income m (the general case)
C Solve the problem. You will obtain solutions x1* (p1, p2, m), x2* (p1, p2, m) in terms of the parameters of the model (p1, p2, m).
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