Help with this problem please.

In the short run, the quantity of output supplied by firms can deviate from the natural level of output if the actual price level deviates from the

expected price level in the economy. A number of theories explain reasons why this might happen.

For example, the sticky$-$wage theory asserts that output prices adjust more quickly to changes in the price level than wages do$,$ in part because of

long$-$term wage contracts. Suppose a firm signs a contract agreeing to pay its workers $$15$ per hour for the next year, based on an expected price

level of $100.$ If the actual price level turns out to be $110,$ the firm's output prices will increase $>,$ and the wages the firm pays its workers will

remain fixed at the contracted level. The firm will respond to the unexpected increase in the price level by raising grad the quantity of output it

supplies. If many firms face similarly rigid wage contracts, the unexpected increase in the price level causes the quantity of output supplied to

$\_$ the natural level of output in the short run.

Suppose the economy's short$-$run aggregate supply $($AS$)$ curve is given by the following equation:

The Greek letter alpha represents a number that determines how much output responds to unexpected changes in the price level. In this case, assume

that alpha$=$$$4$ billion. That is$,$ when the actual price level exceeds the expected price level by $1,$ the quantity of output supplied will exceed the natural

level of output by $$4$ billion.

Suppose the natural level of output is $$40$ billion of real GDP and that people expect a price level of $110.$

On the following graph, use the purple line $($diamond symbol$)$ to plot this economy's long$-$run aggregate supply $($LRAS$)$ curve. Then use the orange

line segments $($square symbol$)$ to plot the economy's short$-$run aggregate supply $($AS$)$ curve at each of the following price levels: $100,105,110,115,$

and $120.$

The short$-$run quantity of output supplied by firms will fall short of the natural level of output when the actual price level

the price

level that people expected.