The economy experiences an increase in the price level and a decrease in real domestic output. Which of the following is the likely explanation?

Answer: Input Prices have increased.
Explanation:
When an Economy sees prices rising but at the same time productivity is falling, the likely cause of that is an increase in Input prices.
Input Prices are the prices of the raw materials and other goods needed to produce finished goods. If these prices should rise, it becomes more expensive for producers to produce and they will therefore reduce the amount of goods they produce. This reduction in Quantity leads to an increase win prices because according to the Law of Supply and Demand, if supply reduces and demand remains the same then prices must increase till a new equilibrium is reached.
For example, imagine a hypothetical Economy of Steel Makers. If the price of Iron changed from $5 to $10, producers who were producing 20 units of Steel will see their costs double and react by producing only 10 units of Steel to maintain cost margins thereby dropping Productivity.
The 20 units of Steel used to be sold in the market at $20 but now that the supply has dropped to 10 units, the price doubles to $40 to cater for this reduction in Quantity.