[Excel Problem] Suppose that we have a neoclassical model. This problem will give specific functional forms for the equations underlying the model. Begin with the supply side. Suppose that labor demand supply are given by:

Nt = a1wt a2t (19.21) Nt = b1wt + b2At + b3Kt is the labor supply curve and (19.22) is labor demand. a1, a2, and b1 b3 are positive parameters.

(a) Use (19.21)-(19.22) to solve for expressions for Nt and wt as a function of parameters and exogenous variables.

(b) Suppose that a1 = 1, a2 = 0.4, b1 = 2, b2 = 0.5, and b3 = 0.3. Suppose further that t = 3, At = 1, and Kt = 20. Make an Excel file to solve for numerical values of Nt and wt using your answer from the previous part.

(c) Suppose that the production function is Yt = AtK t N1 t . Suppose that = 1/3. Use your answer from the previous parts, along with the given values of exogenous variables and parameters, to solve for Yt . Now let us turn to the demand side. Suppose that the consumption and investment demand functions are:

Ct = c1(Yt Gt) + c2(Yt+1 Gt+1) c3rt (19.23)

It = d1rt + d2At+1 + d3Kt (19.24) The aggregate resource constraint is Yt = Ct + It + Gt .

(d) Use the aggregate resource constraint, plus (19.23)-(19.24), to derive an expression for rt as a function of Yt and other variables (for the purposes of this exercises, treat Yt+1 as exogenous). In other words, derive an expression for the IS curve.

(e) Suppose that c1 = 0.5, c2 = 0.4, c3 = 1, d1 = 20, d2 = 0.5, and d3 = 0.1. Suppose further that At+1 = 1, Yt+1 = 1.2, Gt = 0.2, and Gt+1 = 0.2. Given your answer for the value of Yt above, your expression for the IS curve, and these parameter values to solve for numeric values of rt , Ct , and It .

(f) Suppose that At increases from 1 to 1.2. Solve for new numeric values of Yt , Nt , wt , rt , Ct , and It . Do these move in the same direction predicted by our graphical analysis?

(g) Set At back to 1. Now suppose that Gt increases from 0.2 to 0.3. Solve for numerical values of the endogenous variables in your Excel file. Do these variables change in the way predicted by our graphical analysis?