Unformatted text preview: Department of Economics University of California at Berkeley Spring 2002 George Akerlof Andrea De Michelis Economics 202A MIDTERM EXAM Instructions: 1. Be sure to write your name on the cover of each Blue Book. 2. The questions differ in difficulty but count equally. Each question counts 20 points for a total of 80 for the whole exam. 3. Answer all parts to all questions. 1. Show formally from Friedman's model of consumption that there is a positive correlation between transitory and current income. 2. Suppose that Dt = t -5 + t where the t 's are i.i.d. N (0, 2 ). What is Et (Dt +3 ) ? 3. Show that in Mankiw's model (in the absence of a menu cost z) the loss from failure to change price after a constant shift in demand is equal to 2C (where C is the area of the small triangle in Mankiw's key diagram). [Definitions and hints: If q m , p m are the maximizing quantity and price and q n , p n are 1 the non-maximizing quantity and price, C is by definition (q n - q m )( p m - p n ). To answer 2 this question you must specify Mankiw's model, recall what C is, and show that it is equal to 1 the loss in profits.] 2 4. Consider a firm i that minimizes at time t:
j ( ) ( ) 2 1 2 * Et pi ,t + j - p i ,t + j + c( pi ,t + j - pi ,t + j -1 ) , c > 0, j =0 1 + r where pi ,t + j is the log of the nominal price of firm i in period t+j, and p * i ,t + j is the log of the nominal price that firm i would choose in period t+j in the absence of adjustment costs. Costs of changing nominal prices are captured by the second term in the objective function. The information set at time t includes current and lagged pi ,t and p * i ,t . [( ) a. Derive the first order condition of the above minimization problem, giving the current price pi ,t as a function of itself lagged, of its expectation at t+1, and of the current optimal price. b. Rewrite the first order condition using the lag operator. Solve by factorization to derive the following expression:
1 1+ r 1 pi ,t = 1 p i ,t -1 + 2 c j =0 2 E t p * i ,t + j , j 1+ r where 1 and 2 are the reciprocals of the roots of (1 + r ) x 2 - + 1 + r + 1 x + 1 = 0 c and 1 is the smaller of the two. Interpret your result. ! " # $ # % % & ' () ! " " * %% % & " + , ' " " " % , ' . . . /! + ". " . + () ! " " 0 " 1 2 % % () 3 4 % ' ! 6 5 " # % % & - % 7 % & !8 + % % 9 4 :;" $ ...
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