Qualitative analysis of dynamic equations on time scales

In this article, we establish the Picard-Lindelof theorem and approximating results for dynamic equations on time scale. We present a simple proof for the existence and uniqueness of the solution. The proof is produced by using convergence and Weierstrass M-test. Furthermore, we show that the Lispchitz condition is not necessary for uniqueness. The existence of epsilon-approximate solution is established under suitable assumptions. Moreover, we study the approximate solution of the dynamic equation with delay by studying the solution of the corresponding dynamic equation with piecewise constant argument. We show that the exponential stability is preserved in such approximations.Comment: 13 page

Do Money Or Oil And Crop Productivity Shocks Lead To Inflation: The Case Of Pakistan

The worst economic outcomes have been argued as a result of the mismanagement in money supply especially in 1929’s Great Depression, 1970’s Stagflation and 2008’s Economic depression in the global economy. However, economic recessions tend to appear after oil price phenomenon. In particular, the global inflationary pressures of 2008 became severe with the spikes up in oil prices as well as crop productivity shocks in the world economy including Pakistan. The object of the present paper is to discuss inflation in the framework of Monetary and external Oil Price Shocks, Crop Productivity Propositions, Inflation Inertia, and real GDP growth. The empirical studies broadly uphold the monetary explanation of inflation in the Pakistan’s economy. This paper offers the policy implication that the combination of monetary as well as productivity management is required to arrest inflationary pressures in the economy. In addition, we find the comprehensive evidence that food inflation is also a monetary phenomenon in the Pakistan’s economy. On the other hand, the continuous persistence in inflation inertia does not hold as a result of the absence of autocorrelation in money supply in AR (2) or higher process in the data. Oil prices in terms of domestic currency highlight the fact that the transmission channel of world shocks via exchange rate fluctuations leaves significant impacts upon domestic inflation in the economy.Money; Inflation; Oil; Productivity