This economy features a shock to the efciency of new capital produced (aka investment- specic technological change). A rise in q is an improvement in the quality of new capital goods because the same raw units of investment goods have a larger impact on the capital stock used in production. In a competitive equilibrium, q is the ratio of the price of consumption and structures pa relative to the price of equipment pg, i.e. q = gee/pg. You will not need to solve the business cycle version of the model. I will discuss how to do so in. a program later on. (a) (b) (C) (d) {e} (f) (e) What are the state and control variables? Characterize the equilibrium of the economy. The equilibrium conditions involve a resource constraint, labor leisure tradeoff, and two (intertemporal) Euler equations. (Hint: take rst order conditions with respect to Ct,hg,k3,g+1 and kg,g+1 and rear- range. You can follow the logic of the real business model closely but now note that there are two types of investment). Carefully interpret the equilibrium conditions, in particular the intertemporal con dition with respect to investment in capital equipment. Suppose there is a positive realization to at. Describe the transmission of the shock into the economy. Compare the transmission to that of a total factor productivity shock in the standard real business cycle model. Write the steady-state conditions of the model. [Take the equilibrium conditions and remove the time indices. You can simplify by using the rate of time preference r = (1 J/. The steady state can be written as a function of c, kg, k, and 1']. alone, where output satises y = kgakgml-\"s-ae.) The parameter space is 8 = {,5', 6', as, org, 6,, 56}. Solve for the steady state recur- sively. That is, solve for the steady state in a sequence of steps for variables 3:, such that 2:0 = 1MB), :51 = f1{8, 31),... Note that the steady state can be solved without the use of any numerical solver. (Hint: start by solving for the ratio c/kSJ Suppose the law of motion for equipment is k; = (1 63[u))ke + gig where b 54\") = 60 + _uw1w > 1 (.0 Provide intuition on the effects of an endogenous utilization rate on the transmission mechanism. How does a q shock change the utilization rate