Download Sect 1.4b Linear Models

MAC 2233
Section 1.4b
Demand & Supply Functions
THE DEMAND FUNCTION: q(p) = mp + b
q is the demand, the quantity of items buyers will buy, at price p per item. (See blue
box, page 48.)
What do you think happens to q when p goes up?___________________________
THE SUPPLY FUNCTION: q(p) = mp + b
q is the supply, the quantity of items producers will supply, at price p per item.
(See blue box, page 50.)
What do you think happens to q when p goes up?___________________________
EQUILIBRIUM OCCURS WHEN SUPPLY = DEMAND.
A producer or seller likes to sell at the equilibrium price. At this price, no shortage or
surplus occurs.
1. Tasty Grocery is willing to sell 300 cans of canned meat for $.50 a can but will sell 500 cans at
$.75 a can. a. Determine the linear supply function. b. Interpret the slope.
2. One week Tasty Grocery sold 280 cans of meat when the price of one can was $.50. The next
week Tasty Grocery sold 220 cans of meat when the price of one can was $.75. a. Determine the
demand function. b. Interpret the slope. c. Find the equilibrium price. Remember that you found
the supply function in problem 2. d. Use your graphing calculator to draw the graphs of the
supply and demand functions and sketch the graphs. Then use the intersect function to confirm
equilibrium price.
3. a. What happens if you price items to sell above the equilibrium price? b. What happens if you
price items to sell above the equilibrium price?
4. When Tasty Grocery sold canned meat for $.50 a can, 400 cans were sold. When Tasty
Grocery sold canned meat for $.75 a can, 350 cans were sold. Tasty Grocery is willing to supply
300 cans to sell at $.50 a can. Tasty Grocery is willing to supply 400 cans to sell at $.75 a can.
Give the a. linear demand function b. linear supply function. c. Interpret the slopes for each
function.
5. a. At what price does equilibrium occur in problem 4? (Determine this point algebraically and
with the graphing calculator. Sketch graph.) b. What happens if you price each can higher than
the equilibrium price? c. less than the equilibrium price?
6. ACME is willing to sell 800 items for $50 each but is only willing to sell 500 items for $40 each.
Buyers are willing to buy 300 items for $50 each; 400 items for $40 each. Give the a. demand and
b. supply functions. c. Determine the equilibrium price algebraically and with your calculator.
d. Sketch graphs of the two functions.
Assignment: Finish this page and Page 54: 7, 9, 11, 19, 8, 12--On problems 11 and 12, use
your calculator to graph demand and supply functions and check your answer for
equilibrium price by using intersect function. Sketch graph on homework paper.
TO GRAPH AN EQUATION ON CALCULATOR:
1. Y=, enter equation using x for independent variable.
2 a. WINDOW, set appropriate window manually, GRAPH or
. b. WINDOW, select appropriate x values and scale, ZOOM, ZoomFit (will
automatically select appropriate y-values to go with the x-values you entered.
You can “fine-tune” the window if you would like after using ZoomFit. You may only
use ZoomFit when one equation appears on the “Y=” screen.)
TO FIND THE POINT OF INTERSECTION OF TWO LINES USING YOUR CALCULATOR:
1. 2nd TRACE (for calc)
2. 5 (for INTERSECT)
3. ENTER when asked “first curve?”
ENTER when asked “second curve?”
ENTER when asked “guess?”
Sect. 1.4b Worksheet Answers
1a) q(p) = 800p – 100
b) For each $1 increase in price of a can of meat, the grocery
is willing to supply 800 more cans to sell.
2a) q(p) = -240x + 400
b) For each $1 increase in price of a can of meat, the demand—
number of items sold—will decrease by 240. c) $.48
3a) You will have a surplus of items in inventory. b) You will have a shortage of items to sell.
4a) q(p) = -200p + 500
b) q(p) = 400p + 100
c) like b in 2 and 3.
5a) $.67 b) You will have a surplus of cans to sell c) You will have a shortage of cans to sell.
6a) q(p) = -10p + 800
b) q(p) = 30p – 700
c) $37.50
(054)