Final answer:
Expectations of currency depreciation lead to an increase in supply and a decrease in demand for that currency, lowering its value. If the expectation is for appreciation, there is a decrease in supply and an increase in demand, raising the currency's value.
Step-by-step explanation:
When there is an expectation of depreciation in the US dollar compared to the European Euro, this can lead to a change in the behavior of investors and consumers. They tend to divest from the currency that is expected to lose value, thus increasing the supply of dollars in the market while the demand for that currency decreases. This can be graphically shown by a rightward shift in the supply curve for dollars and a leftward shift in the demand curve for dollars, leading to a decrease in the US dollar's value relative to the Euro.
If the expectation was reversed, and there was an anticipation of an appreciation of the US dollar, the behavior would be the opposite. People would be more likely to hold on to or acquire more dollars in expectation of future gains, leading to a decrease in supply and an increase in demand. This would be shown by a leftward shift in the supply curve and a rightward shift in the demand curve, resulting in an increase in the dollar's value compared to the Euro.