Tom consumes only beer (B) and whisky (W). His utility function is U(B,W) = 2B + 5W, where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 2, the price of whisky is PW = 5, and Tom’s income is M = 20 dollars. (a) Obtain the equation of Tom’s indifference curve for the utility U > 0 with beer in the horizontal axis and whisky in the vertical axis. What is the magnitude of the slope of Tom’s indifference curves? Explain the economic meaning of this magnitude. Are Tom’s indifference curves vertically parallel? Explain. (b) Obtain the equation of Tom’s budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Does Tom consume beer at the current prices (indicated above)? Explain in detail. (c) Are Tom’s preferences quasi-linear? Are they homothetic? Justify each of your answers. (d) Tom’s brother, Jerry, has a utility function given by V (B, W ) = max{B, W }. (d.1) Are Jerry’s preferences convex? Are they strictly convex? Justify your answers. (d.2) Are Jerry’s preferences complete? Explain. (d.3) Are Jerry’s preferences transitive? Explain.
Tom consumes only beer (B) and whisky (W). His utility function is
U(B,W) = 2B + 5W,
where B is the quantity of beer and W is the quantity of whisky. The price of beer is PB = 2, the price of whisky is PW = 5, and Tom’s income is M = 20 dollars.
(a) Obtain the equation of Tom’s indifference curve for the utility U > 0 with beer in the horizontal axis and whisky in the vertical axis. What is the magnitude of the slope of Tom’s indifference curves? Explain the economic meaning of this magnitude. Are Tom’s indifference curves vertically parallel? Explain.
(b) Obtain the equation of Tom’s budget line. What is the magnitude of the slope of the budget line? What is the economic interpretation of this magnitude? Does Tom consume beer at the current prices (indicated above)? Explain in detail.
(c) Are Tom’s preferences quasi-linear? Are they homothetic? Justify each of your answers.
(d) Tom’s brother, Jerry, has a utility function given by
V (B, W ) = max{B, W }.
(d.1) Are Jerry’s preferences convex? Are they strictly convex? Justify your answers.
(d.2) Are Jerry’s preferences complete? Explain. (d.3) Are Jerry’s preferences transitive? Explain.
Step by step
Solved in 3 steps with 2 images
