Chapter 3.3, Problem 14E

Market Demand This is a continuation of Exercise 13. The following table shows the quantity D of wheat, in billions of bushels, that wheat consumers are willing to purchase in a year at a prince P, in dollars per bushel.

D $=$ quantity of wheat	P = price
$1.0$	$\$2.05$
$1.5$	$\$1.75$
$2.0$	$\$1.45$
$2.5$	$\$1.15$

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

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

b. Add the graph of the linear formula you found in part a, which is called the market demand curve, to your graph of the market supply curve from Exercise 13.

c. Explain why the market demand curve should be decreasing.

d. The equilibrium price is the price determined by the intersection of the market demand curve and the market supply curve. Find the equilibrium price determined by your graph in part b.

13. 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?