please give me the answers to these questions!thank you so much! question1. answer the required for belowing utility functions U = 2x1+3x2 U =

please give me the answers to these questions!thank you so much!

question1. answer the required for belowing utility functionsU = 2x1+3x2U = 4x1+6x2U = x1x2

MU1=?

MU2=?

MRS=?

Diminishing MRS?yes or no?

question2. Apu is in the habit of drinking beer each evening while watching TV. She does notcare about the size of the cans that the beer comes in: she only cares about how much beer shedrinks. Draw some of Apu’s indifference curves between 16oz cans of beer and 8 oz cans. Labelyour axis, clearly mark any points of importance, and indicate which curves are associated withhigher utility.

question3. Consider your tastes for five dollar bills and ten dollar bills (and suppose that youcould have partial $10 and $5 bills). Suppose that all you care about is how much money youhave, but you don’t care whether a particular amount comes in more or fewer bills.(a) With the number of five dollar bills on the horizontal axis and the number of ten dollarbills on the vertical, illustrate three indifference curves from your indifference map.(b) What is your marginal rate of substitution of ten dollar bills for five dollar bills?(c) What is the marginal rate of substitution of five dollar bills for ten dollar bills?(d) Are averages strictly better than extremes? How does this relate to whether your tastesexhibit diminishing marginal rates of substitution?

question4. Let's consider some logical relationships between preferences and types of goods.Suppose you consider all the goods that you might potentially want to consume.(a) Is it possible for all these goods to be luxury goods at every consumption bundle?(b) Is it possible for all goods to be inferior goods at every consumption bundle? Is itpossible for all of them to be normal goods?(c) True or False: When tastes are homothetic, all goods are normal goods.(d) True or False: In a two good model, if the two goods are perfect complements, they mustboth be normal goods.

question 5.Consider the utility maximization problem subject to a budget constraint with thefollowing utility function: U(x, y) = 8x0.5y1.5 and the associated MRS is y/3x. Assume that Px isthe price of x, Py is the price of Y and I is the consumer’s income.(a) Are the Marshallian demand functions scale invariant (i.e. homogeneous of degree zero)?(b) Are the goods Giffen?(c) Show why or why not the goods are inferior or normal.

question6. Suppose a consumer’s tastes are described by the utility function above in #7.Suppose currently Px=$2.50 and Py=$3.33 and the consumer has a fixed exogenous income I=40.(a) Find the values of X*, Y*, and the maximum utility that the consumer attains at thisoptimal bundle.(b) Now suppose that Px decreases to Px=$2.00. Calculate the substitution effect.(c) Calculate the income effect.