3. Consider the U-functions below:

i)U(X,Y) = 4X²Y³ with = 8Y³ and = 12²².

ii)U(X,Y) = 4X+3Y

iii)U(X,Y) = min(4X,3Y)

Find the MRSxy for each of them and comment. Try to plot the indifference maps for these U-functions. Find the demand equations for X and Y for all the above i-iii curves using income I, price of X as Px and price of Y as Py. What about U(X,Y) =4X - 3Y?

4. Sharon has the following utility function: U=x1/2 + y1/2 where x is her consumption of candy bars and y is her consumption of espressos. Given that utility function, her = 0.5and her = 0.5. Use "I" for income.

a)Derive Sharon's demand functions for candy bars and espressos (note that a demand function will be a function of Px or Py, given I such as X = f(Px, Py, I); hint: you might need to use the technique of squaring both sides of an equation to get rid of square roots. This exercise might require you to revise maths fundamentals of simplification, manipulation and exponents.)

b)Assume that Px=$1, Py=$3, and income I=$100. Draw her budget line. How many candy bars and espressos will Sharon consume? What is her level of utility at this amount?

c)Now suppose the price of espressos (y) goes up to $4, price of candy bars (x) and her income (I) remaining unchanged at part b. level. How many candy bars and espressos will Sharon consume? What is her level of utility at this amount?

d)What can you say about Sharon's preference from the above findings?

5. a. Draw indifference maps to represent Jill's preferences over the two commodities, x and y, in the following cases. What assumptions did you have to make? Comment on the MRSxy for each case:

i)x = money, y = air pollution.

ii)x = bitcoins, y = government bonds; if a. Jill does not like taking risk at all, b. Jill really enjoys the thrills of taking risk and c. if Jill likes to take risk but up to a certain limit beyond which she absolutely dislikes risks.

iii)x = 500g pack of sugar, y = 250g pack of sugar.

iv)x = waffles, y = ice cream; and Jill will consume waffles (x) only with ice cream (y).

v)x = electronic devices, y = all other goods

Suppose the budget line is I = Px.X + Py.Y. Indicate on your maps where the utility maximizing solution will be reached for the 5 cases above.

b. For 5a.v, what happens to the budget line if the government applies a tax of $1 on the price of all electronic devices but does not tax other goods? What would be an "equivalent" income tax on your diagram? Is this the same as equivalent variation?