Los depósitos circulares como modelo de prueba de la tecnología del pretensado

The equilibrium system can be viewed from an aggregate demand-aggregate supply (AD-AS) perspective, which is useful to clarify the concepts of demand and supply.

Real Aggregate Demand

The household’s consumption condition (2.14) characterizes the consumption demand, which describes a negative contemporaneous relationship between the price in utils ˆλ_t and consumption ˆct.

Substitute the capital law of motion (2.21) into the firm’s investment condition (2.19).

We get an equation that characterizes the investment demand, which describes a negative contemporaneous relationship between the price in utils ˆλ_t and investment ˆi_t:

ˆλ_t= −z_iβwl k ζ

δˆi_t+ (1 − δ) ˆk_t

+ Et(Θ_t+1) + Ψ_t, (2.29)

where Θt+1is a combination of future prices and output and Ψtis a combination of various exogenous shocks.⁴

Combining the consumption demand condition (2.14), the investment demand condition (2.29), and the aggregate resource constraint (2.22) gives us the real aggregate demand (AD) condition which describes a negative contemporaneous relationship between the price in utils ˆλ_t and the aggregate demand ˆyt.

Monetary Aggregate Demand

Combining the Fisher’s equation (2.23) and the monetary policy (2.24) gives us the mon-etary AD condition

φ_πΠˆ_t= −φ_yyˆ_t+ ˆλ_t+ Et ˆΠ_t+1− ˆλ_t+1

− ˆβ_t− ˆz_m,t, (2.31)

which describes a negative contemporaneous relationship between the monetary price ˆΠt

and the aggregate demand ˆy_t.

Aggregate Supply

The aggregate supply (AS) condition can be obtained by combining the firm’s pricing condition (2.17), the required labor for production (2.20), and the household’s labor supply condition (2.15): which shows a positive contemporaneous relationship between the price in utils ˆλ_tand the aggregate supply ˆyt. If prices are sticky (φp > 0), the AS condition (2.32) also shows a positive contemporaneous relationship between the monetary price ˆΠ_t and the aggregate supply ˆyt. Hence, the AS condition is also known as the New Keynesian Philips Curve (NKPC) in the business cycle literature (e.g., Woodford, 2005).

Reduced Equilibrium System

The equilibrium system can now be reduced to a stable stochastic process of four variables (ˆyt, ˆλt, ˆΠt, and ˆkt+1) that satisfies the real AD condition (2.30), the monetary AD condition (2.31), the AS condition (2.32), and the law of motion for capital (2.21).

For a given set of state variables, the short run equilibrium is characterized by ˆy_t, ˆλ_t, and ˆΠt, and is pinned down by the real AD (2.30), the monetary AD (2.31), and the AS (2.32) conditions, which are surfaces in the output-price in utils-monetary price space.

For example, Figure 2.1 shows these three surfaces in a standard one-good economy. The upper right panel of Figure 2.1 shows that a positive shock to the nominal interest rate moves the monetary AD surface inward, causing a lower inflation rate. The intersection of the real AD surface and the monetary AD surface projected on the output-price in utils plane gives us a downward sloping real AD curve. Since the real AD surface is orthogonal to the output-price in utils plane, a shift in the monetary AD surface has no effect on the real AD curve. The intersection curve of the AS surface and the monetary AD surface projected on the output-price in utils plane gives us an upward sloping real AS curve.

When there are nominal rigidities, moving the monetary AD surface inward would cause a lower output and move the real AS curve to the left.

AD-AS System

Figure 2.1: The solid surfaces and the solid lines represent a standard one-good economy in steady state. The dotted surface and the dashed lines represent the same one-good economy with a positive shock to the nominal interest rate that shifts the monetary AD surface inward. Each line on a surface is the intersection line of the surface and the monetary AD surface.

Demand and Supply

Definition 2.2. (Demand shocks and supply shocks) A real demand shock is a shock that disturbs the real AD condition (2.30). A monetary demand shock is a shock that disturbs the monetary AD condition (2.31). A supply shock is a shock that disturbs the AS condition (2.32).

I now classify the eight exogenous shocks based on the above definition.

An increase in the marginal utility of consumption ˆz_c,t is a positive real demand shock as it increases the consumption demand.

An increase in the dis-utility of labor ˆω¯_t is a negative supply shock as it reduces the labor supply.

An increase in patience ˆβt is both a positive real demand shock as it increases investment demand and a negative monetary demand shock as it creates a deflationary pressure by

making money hoarding more attractive.

An increase in the labor demand elasticity ˆεw,t, which is similar to a decrease in the labor dis-utility, is a positive supply shock as it increases the supply of labor by lowering the wage markup.

An increase in the goods demand elasticity ˆεp,t is a positive supply shock as it lowers the price-cost markup. In addition, if the increase in the goods demand elasticity ˆε_p,t is persistent, the expected increase of ˆεp,t+1 is also a positive real demand shock as it increases the investment return by reducing the price-cost markup in the future.

An improvement in the investment specific technology ˆz_i,t could be a positive or a negative real demand shock depending on the parameter values. On one hand, the improved in-vestment specific technology lowers the cost of inin-vestment and boosts inin-vestment demand.

On the other hand, the improved investment specific technology makes the investment more efficient; thus, less investment is required to achieve the desired capital level in the future. For example, if the convexity of the variable cost function in steady state ζ is low enough, the first effect dominates and the improved investment specific technology works as a positive real demand shock. However, if ζ is sufficiently high, the second effect dom-inates and the improved investment specific technology becomes a negative real demand shock.

An increase in the labor productivity ˆz_l,t is clearly a positive supply shock.

Finally, an increase in the nominal interest rate ˆz_m,tis a negative monetary demand shock as it creates a deflationary pressure.