The existing literature is clear that low income economies tend to suffer from foreign exchange shortages exacerbated by their exports. Most importantly, the concentration of their exports renders these countries susceptible to international price fluctuations. This frequently affects the level of foreign exchange, causing excess demand for foreign exchange leading to foreign exchange shortages. Using a four-sector New Keynesian dynamic stochastic general equilibrium (DSGE) model with foreign exchange constraints faced by importing rms, we calibrate the model to Malawian economy to investigate the implications of foreign exchange constraints on key macroeconomic variables in low income import dependent economies. We demonstrate that imports are a vital part of the production process for LIEs and determine the response and direction of output and consumption. Second, the degree of the foreign exchange constraint determines the degree of variability of the shock, but, does not change the direction of the shock. Third, increasing imports in an effort to increase productivity reduces output and consumption and induces a depreciation of the exchange rate. Fourth, the model illustrates that the domestic contractionary monetary policy produces the conventional results on output, consumption and other variables.