Value of Commitment [Intermediate] From now on, we demonstrate the value of commitment to low ination. Argue that if there was no monopolistic power, output would be eicient and equivalent to: w = [1/911/5. Hint: setup the Lagrangian of the planner's problem and take the rst order condition with respect to L and the replace the production function. (h) [Hard] For this question, you ust read chapter 15.2. We now consider a game between the government and the private sector. We assume that p, rms can chose the ideal price: I _ i w P '7 _ 1 the other set of rms is stuck at a given price, chosen in advance, given the expectation of 191, that is E [p1]: p3 =]E[p1]HL' . L. n 1 Recall that: 191 = #pf + (1 - ms. Show that if the government wants to target , we have that: W 3 = IE . _ P [P1 1'? _ 1 And using: 191 = #pf + (1 Mpg, show that: J p. = \"*1 IE [w] 1 - (1 - u) 31% (i) [Hard] Show that for any choice of E [w], the government would want to surprises rms with even higher wages. What are the consequences of this? Do you think this type of behavior can lead to an ever increasing spiral of ination. What would be the effects on output if an inationary Spiral is expected