Adam consumes only beer (B) and whisky (W). His utility function is U(B,W) = B+5W, where...

  

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Adam consumes only beer (B) and whisky (W). His utility function is U(B,W) = √B+5√W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 5, the price of whisky is Pw = 40, and Adam's income is M = 100 dollars. (a) Obtain the equation of Adam's indifference curve for the utility level = 6, with the quantity of whisky as a function of the quantity of beer. (b) Obtain the amount of whisky required to attain the utility level U = 6 if the amount of beer is B = 1? Compute the marginal rate of substitution (MRS) at that bundle and explain how you interpret that magnitude (of the MRS). (c) Obtain the equation of Adam's budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? (d) Adam's cousin, John, has a utility function given by V(B,W) = 3B2+W². (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 answere (d.3) Do John's preferences satisfy the diminishing marginal rate of substitution property? Explain (d.4) Assume that the prices are as indicated above (PB = 5 and Pw income is I > 0. Obtain John's optimal bundle. 40), and John's Adam consumes only beer (B) and whisky (W). His utility function is U(B,W) = √B+5√W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 5, the price of whisky is Pw = 40, and Adam's income is M = 100 dollars. (a) Obtain the equation of Adam's indifference curve for the utility level = 6, with the quantity of whisky as a function of the quantity of beer. (b) Obtain the amount of whisky required to attain the utility level U = 6 if the amount of beer is B = 1? Compute the marginal rate of substitution (MRS) at that bundle and explain how you interpret that magnitude (of the MRS). (c) Obtain the equation of Adam's budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? (d) Adam's cousin, John, has a utility function given by V(B,W) = 3B2+W². (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 answere (d.3) Do John's preferences satisfy the diminishing marginal rate of substitution property? Explain (d.4) Assume that the prices are as indicated above (PB = 5 and Pw income is I > 0. Obtain John's optimal bundle. 40), and John's