Chapter 1 Section 3

Excel Companion Chapter 1 section 3

Linear Supply and Demand - Sheet Rock

Open the file LinSD.xls and click the tab for Linear Supply and Demand.

SITUATION: Sheet rock manufacturers are at the mercy of the marketplace since there are alternatives to using sheet rock in home building. If suppliers raise the price too much, consumers will buy less or choose different materials. If the price is low enough compared to other materials, consumers will buy a great deal. If the price is set too low then suppliers may decide to produce less until conditions change. From the consumers’ perspective, higher prices for sheet rock are associated with lower demand. From the producer’s perspective, higher prices for sheet rock are associated with higher quantities that they are willing to supply.

During the spring, demand for sheet rock in a certain community ranges from 6,000 to 12,000 sheets. Units are given in thousands. Experience has shown that at a price of $15.50 per sheet, the demand falls to 6.75 units. The demand rises to 10.75 units at a price of $3.00 per sheet. On the other hand, many manufacturers cannot make much of a profit at $3.00 so the supply drops to 2.25 units. The suppliers can make a very good profit at $15.50 per sheet so the amount available jumps to 15.75 units. Assume that the relationship between quantity and price is linear for both supply and demand.

The sheet graph and table in LinSd.xls displays a demand function (green) and a supply function (blue).

LinSD.xls - Linear Supply and Demand

Economists currently think of quantity demanded or quantity supplied as a function of price. Historically, however, they put price on the vertical axis and quantity on the horizontal axis and this has remained the economic tradition for labeling the axes of supply and demand functions. A theoretical economics assumption is that market forces will cause quantity and price to approach an equilibrium point. The equilibrium point for the sheet rock situation is the intersection of the two graphs. The unique point where the two linear graphs cross can be calculated algebraically from the system of two linear equations in two variables.

QUESTIONS:

1.	The slope of the line through points and is
	Determine the slope of the line through the two given points (6.75, 15.50) and (10.75, 3.00) on the linear demand function.
2.	Using the variable p, for price in dollars, and the variable q, for quantity in thousands, write an equation for this demand function.
3.	Determine the slope of the line through the two given points (2.25, 3.00) and (15.75, 15.50) on the linear supply function.
4.	Write an equation for this supply function.
5.	Find the point of intersection algebraically and compare your results with the table in graph & table.
6.	Give a verbal interpretation of the point found in #5.

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