Question

1. Answer four of the following. In each case answer True, False or Uncertain and explain your answer. Limit each answer to one page. A firm has a technology that relies on only one input (call it x). The output of the firm(call it y) increases as you increase x but at a diminishing rate. Based only on the information provided thern y-100 exp(-x) would be a valid representation of this firm's production function. (a) (b) Consider a person who begins day 0 with a 5mm sheet of paper. On day one she folds the piece of paper in half. Each day that follows she continues to fold the new piece in half- one fold each day. The thickness of the paper after N days is given by the formula (.5*2"N) and the thickness of the paper after 40 days will be 40mm Suppose you had the option of living in country A or country B. The interest rate in A is 5% and the interest rate in B is 300, all other conditions in the two countries are identical. In A you will receive a payment of 2500 every year, while in country B you will receive 1500 each year. You would prefer to live in country A. (For simplicity assume that you will live forever). (c) (d) Suppose the amount of cigarettes an individual smokes today (C) is given by the relationship C-S-P where P is the price of cigarettes and S is the stock of cigarettes smoked in the past. Since 86 δΡ65 this means that neither the price of cigarettes or the stock of cigarettes smoked in the past has any effect on today's consumption. e) A consumer has a utility function defined over income x given by U(x)-In(x). This individual is risk neutral.

Answer 1

y = 100 middot e^-x, Partialdifferential y/Partialdifferential x = -100 middot e^-x, Partialdifferential^2 y/Partialdifferential x^2 = + 100 middot e^-x Thus o/p downarrow, as x uparrow & at an uparrowing Rate False thickness after N days (t) = .5 times 2 times N day 2, t = .5 times 2 times 2 = 2 day 4 t = .5 times 2 times 4 = 4 thus False i_A = 5%, i_B = 3 %, payment of 2500/year in Nation A of 1500/year in Nation B True c = s - p, Partialdifferential c/Partialdifferential s = 1, Partialdifferential^2 c/Partialdifferential p Partialdifferential s = 0, Partialdifferential/Partialdifferential p (Partialdifferential c/Partialdifferential s) = 0 as stock of cigarettes smoked in past uparrow, today's cons uparrow, since Partialdifferential c/Partialdifferential p = -1, as Price uparrow, Partialdifferential c/Partialdifferential p < 0, thus c downarrow Partialdifferential c/Partialdifferential s > 0, False u (x) = ln x, Partialdifferential u/Partialdifferential x = 1/x