Question

PC -MR diagram to show the logic behind the equation (best response Taylor rule) Approach the question as follows: (a) Use the diagrams to show how the initial interest rate response to an inflation shock varies with the slope of the MR. (b) What parameters affect the slope of the MR? (c) Are your findings consistent with the best response Taylor rule equation?

Answer 1

Ans (a) A Taylor Rule is a policy rule that tells the central bank how to set the current interest rate in response to shocks that results in deviations of inflation from target or output from equilibrium or both. In other words, (r₀ -r_s) responds to.$\pi ^{0}-\pi^{T}$ .On the basis of an empirical analysis of the behavior of the US Federal Reserve, Taylor puts the weights on the two deviations.

Now, we can investigate how the coefficients on the inflation and output deviations depend on the slopes of the curves, we shall see that if the absolute value of the slope of the IS, the Philips curve and the MR are each equal. This helps bring out the role that differences in economic structure (demand and supply sides ) and in central bank preferences can have on the coefficients of Taylor rules.

To see how the central bank should react now to a signal from current economic data about inflation and output, it is necessary to state clearly the lags between the variables. It is assumed that there is no observational time lag for the monetary authorities. i.,e the central bank can set the interest rate (r₀) as soon as it observes the current data ($\pi {0}$ and y0).

The two components of our Taylor rule are shown by the vertical distances equal to $\pi {0}$ - $\pi ^{T}$ . $\alpha$ is the slope of the Philips curve. Just one more step is needed to express this forecast in terms of (r₀ - rs) and therefore to deliver a Taylor rule.

_{Thus, we have $r_{0}-r^{s} = 1/[\alpha }(\alpha +1/\alpha \beta )](\pi _{0}-\pi {r})$}

It is important to note that in the case of three kinds of shocks examined above i.e, an inflation shock that shifts the Philips curve (or the analytically identical case in the IS -PC -MR model of a change in monetary policy that shifts the inflation target, an aggregate demand shock that shifts the IS or an aggregate supply shock that shifts the equilibrium level of output , the period zero effect is either a deviation of output from equilibrium or a deviation of inflation from target, but not both.

Ans (b) Marginal Revenue is the additional revenue that will be generated by increasing product sales by one unit. It can also be described as the unit revenue the last item sold has generated for the firm. In a perfectly competitive market, the additional revenue generated by selling an additional unit of a good is equal to the price the firm is able to charge the buyer of the good This is because of a firm in a competitive market will always get the same price for every unit it sells regardless of the number of units the firm sells since the firm's sales can never impact the industry's price. However, a monopoly determines the entire industry's sales. As a result, it will have to lower the price all units sold to increase sales by 1 unit. Therefore, the marginal revenue generated is always lower than the price the firm is able to charge for the unit sold since each reduction in unit price causes unit revenue to decline on every good the firm sells.

The marginal revenue curve is affected by various factors such as the demand curve-changes in income, changes in the prices of complements and substitutes, changes in population. These factors can cause the R curve to shift and rotate.

Ans (c) YES, the findings are consistent with the best response Taylor Rule equation.