Find the Marginal Rate of Substitution (MRS) for the following utility functions:

a. U(X,Y) = X0.3Y0.4

b. U(X,Y) = XaY1-a

2. Suppose a consumer has the following utility function: U(x1,x2) = alnx1 + (1-a)lnx2

a. Use the Lagrange method to find the demand functions for x1 and x2

b. Suppose the price of good 1 is $10 and the price of good 2 is $20 and the consumer’s

income is $500. Find the quantities of x1 and x2 if a=1/2.

3. A consumer has the following utility function: U(X1,X2) = X1X2 + 3X1 + X2

Where X1 is her consumption of pastries with a price of $8 and X2 is her consumption of books

with a price of $12. Her income is $212. Determine the number of pastries and books that will

maximize the consumer’s utility.

4. A consumer has the following demand function for good 1: x1 = (3/4)(m/p1)

The original price of the good is $2 and the consumer’s income is $200. Calculate the substitution

effect, the income effect and the total effect for this consumer, when the price of good changes to

$1.

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