Obtain the equation of the indifference curve for the utility level U = 20 (set min the vertical axis). Is this indifference curve steeper than the indifference curveyou derived in part (a)? Explain.3

Cobb-Douglas Preferences Specific Example: Consider the util-ity function U (x, y) = x 0.5 y 0.5 that is defined on the consumption setR 2+ .(a) Find the equation of the indi↵erence curve that corresponds toU = 40.(b) What is the slope of the indi↵erence curve for U = 40 for anygiven value of x?(c) What is the equation of an arbitrary indi↵erence curve for thisutility function?(d) What is the slope of an arbitrary indi↵erence curve for this util-ity function at any given value of x?

U(x, y) = (3x + 2y)2 .The price of x is px = $10 per unit and his income is $200.(a) Obtain the equation of Johnathan’s indifference curve for the utility level U = 100. Drawthis indifference curve. (2 marks)(b) The price of y is py = $8 per unit. Obtain the marginal rate of substitution (MRS) and theequation of the budget line. Using a graph, find Johnathan’s optimal consumption bundle.In this graph, show the budget line, the optimal bundle, and the corresponding indifferencecurve. Make sure to label carefully all the curves. (3 marks)(c) Suppose that the price of y drops to py = $6 per unit (the price of x remains the same,at px = $10 per unit, and the income remains the same). Obtain the equation of the newbudget line. Using a new graph, find Johnathan’s optimal bundle with this new price. Inthis graph, show Johnathan’s new budget line, new optimal bundle, and the correspondingindifference curve. Make sure to label carefully all the curves. (3 marks)(d) Now suppose that the price of y is py = $8 per unit if Johnathan buys less than 10 units ofthis product, and py = $6 per unit if he buys 10 units of y or more (as an example, 20 unitsof y would cost $120). Assume that the price of x remains the same, at px = $10 per unit.Derive the equation of the budget line and draw it in a separate graph. (3 marks)(e) Using a new graph, find the optimal bundle(s) for the problem in part (d). In this new graph,show the budget line, the optimal bundle and corresponding indifference curve. Make sureto label carefully all the curves. (3 marks)

Suppose the demand curve for a product is vertical and the supply curve is upward sloping. If a unit tax is imposed in the market for this product,

Question 1 (22 marks). Adam consumes only beer (B) and whisky (W ). His utility function isU (B, W ) = √B + 5√W ,where B is the quantity of beer and W is the quantity of whisky. The price of beer is P B = 5, theprice of whisky is P W = 40, and Adam’s income is M = 100 dollars.(a) Obtain the equation of Adam’s indifference curve for the utility level U = 6, with the quantityof whisky as a function of the quantity of beer. (2 marks)(b) Obtain the amount of whisky required to attain the utility level U = 6 if the amount of beeris B = 1? Compute the marginal rate of substitution (MRS) at that bundle and explainhow you interpret that magnitude (of the MRS). (4 marks)(c) Obtain the equation of Adam’s budget line. What is the magnitude of the slope of thebudget line? What is the economic interpretation of this magnitude? (4 marks)(d) Adam’s cousin, John, has a utility function given byV (B, W ) = 3B 2 + W 2 .(d.1) Are John’s preferences monotone? Are they strictly monotone? Justify your answers.(3 marks)(d.2) Are John’s preferences convex? Are they strictly convex? Justify your answers. (3marks)(d.3) Do John’s preferences satisfy the diminishing marginal rate of substitution property?Explain. (2 marks)(d.4) Assume that the prices are as indicated above (P B = 5 and P W = 40), and John’sincome is I > 0. Obtain John’s optimal bundle. (4 marks)EXAMINATION CONTINUES ON NEXT PAGE1

The slope of a demand curve depends on