Chapter 3.3, Problem 13E

Market supply The following table shows the quantity $S$ of wheat, in billions of bushels, that wheat supplies are willing to produce in a year and offer for sale at a price $P$, in dollars per bushel.

S $=$ quantity of wheat	P = price
$1.0$	$\$1.35$
$1.5$	$\$2.40$
$2.0$	$\$3.45$
$2.5$	$\$4.50$

In economics, it is customary to plot $S$ on the horizontal axis and $P$ on the vertical axis, so we will think of $S$ as a variable and of $P$ as a function of $S$.

a. Show that these data can be modeled by a linear function, and find its formula.

b. Make a graph of the linear formula you found in part a. This is called the market supply curve.

c. Explain why the market supply curve should be increasing. (Hint: Think about what should happen when the price increases.)

d. How much wheat would suppliers be willing to produce in a year and offer for sale at a price of $\$3.90$ per bushel?