Marginal Rate of Substitution from The Cobb-Douglas
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
Marginal Rate of Substitution from The Cobb-Douglas
Problem Set 1 (due March 8) Problem 1 Check whether the following preference relations…1 answer below »
Problem Set 1 (due March 8) Problem 1 Check whether the following preference relations on R2 + satisfy the properties of transitivity, monotonicity, convexity: x ? y ? x1 + x2 = y1 + y2
x ? y ? max{x1,x2} = max{y1,y2} Problem 2 Suppose that John has the following preference relation over two goods, bread and bear (x1, x2). He strictly prefers any bundle x over y whenever x contains more bear than y, whatever the quantity of bread. If the two bundles contain the same amount of bear, he prefers the bundle containing more bread. Find John’s indifference curves on the space R2 +.
Problem 3 Prove that, if a preference relation >- is represented by the utility function u(x1, x2) = x1x2, then >- is convex. Problem 4 John and Mary have two different preference relations over eating pizza and going to the beach (leisure time). These preferences are represented by the following utility functions
uJ = vx1 + x2, uM = 2vx1 + x2,
where x1 are pounds of pizza and x2 is time spent in the beach. Assume also that they can both spend a minimum of zero and a maximum of 8 hours in the beach, and that, when they are not in the beach they spend their time working. Draw John and Mary’s consumption set and their indifference curves. Now suppose that you have to select either John or Mary for a Job. Is John more or less likely to be a hard worker than Mary?
Problem 5 Compute the marginal rate of substitution from the Cobb-Douglas utility function
u(x1,x2) = vx1x2 and find the equation defining the indifference curves Problem 6 Compare the following utility functions: u(x) = vx1x2, w(x) = x1x2. How can you compare the preference relations that each one of them is representing? Problem 7 Suppose you go to the market to buy apples (x1) and oranges (x2) and discover that the price of apples is 1 euro per unit and the price of oranges is 1 per unit when you buy less than 20. If, instead, you buy 10 or more oranges, the price falls to 0.75 euro each. Assuming that your money income is 40, draw the budget line.
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