Linear demand:
Qd = a – bP
Qd: quantity demanded
a; autonomous level of demand (e.g. unrelated to price changes)
b: is the responsiveness of consumers to a change in price – this is the slope
P: price
· We basically see that Qd is a function (“a result of a change in”) the price of the good; ∆P → ∆Qd (and we also see that our axes are wrong in the model!)
· Assume that our D function is Qd = 4,000 – 20P
o At P=0 Qd will be 4000 units
o At P=200 Qd is zero units
P / Qd / Calculation0 / 4000 / Qd = 4,000-20*0; 4,000
50 / 3000 / Qd = 4,000-20*50; 3,000
100 / 2000 / Qd = 4,000-20*100; 2,000
150 / 1000 / Qd = 4,000-20*150; 1,000
200 / 0 / Qd = 4,000-20*200; 0
o Every incremental increase in price of $50 leads to a decrease in Qd of 1,000 units
Shifting the D-curve (e.g. what happens when a non-P variable affecting demand changes)
· Recall that our demand function is Qd = a – bP
· An increase in demand means that Qd increases at ALL PRICE LEVELS
o This means that autonomous demand changes (‘a’)
o The new D function is Qd = 5,000 – 20P
o At P=0 Qd will be 5,000 units
o At P=250 Qd is zero units
P / Qd / Calculation0 / 5000 / Qd = 5,000-20*0; 5,000
50 / 4000 / Qd = 5,000-20*50; 4,000
100 / 3000 / Qd = 5,000-20*100; 3,000
150 / 2000 / Qd = 5,000-20*150; 2,000
200 / 1000 / Qd = 5,000-20*200; 1,000
o Note that every incremental increase in price of $50 still leads to a decrease in Qd of 1,000 units – e.g. the slope has not changed.
o
Changing the slope of the D-curve
· So, our original demand function is Qd = a – bP
o which is Qd = 4,000 – 20P
· If the slope changes from 20 to 15, e.g. Qd = 4,000 – 15P…
o The slope becomes steeper
o The D-curve will intercept the P-axis at….
Changing the slope from 20 to 15P / Qd / Calculation
0 / 4000 / Qd = 4,000-15*0; 4,000
50 / 3250 / Qd = 4,000-15*50; 3,250
100 / 2500 / Qd = 4,000-15*100; 2,500
150 / 1750 / Qd = 4,000-15*150; 1,750
200 / 1000 / Qd = 4,000-15*200; 1,000
· If demand decreases and the slope also decreases…
o The new function is Qd = 3,000 – 30P
o Any change in a non-P variable can affect both ‘a’ and ‘b’ in the D function
§ A change in ‘a’ means that demand has changed…(i.e. a change in a non-P variable!)
§ And a change in ‘b’ means a change in the responsiveness to a change in price (as in availability/closeness of substitutes)
Changing the slope from 20 to 30 and a ↓DP / Qd / Calculation
0 / 3000 / Qd = 3,000-30*0; 3,000
50 / 1500 / Qd = 3,000-30*50; 1,500
100 / 0 / Qd = 3,000-30*100; 0
150 / -1500 / Qd = 3,000-30*150; -1,500
200 / -3000 / Qd = 3,000-30*200; -3,000
Simple worksheet
Both Mr Steele and I are a bit uncertain about precisely is to be expected on exam questions but we are about 90% certain that the basic exercises below cover it. Note that calculations such as you will do in S&D will return several times in later sections!
1. Starting with a D-function of Qd = 200 – 2P
a. This tells us that
i. The Q-intercept is 200
ii. The P-intercept is 200/2 is 100
2. Make a simple table showing the Qd when P=100, 75, 50, 25 and 0
3. Illustrate these values (pairs) in a diag, e.g. draw a D-curve
4. Draw a new diagram based on the price of a complement decreasing – this leads to a 20% change in demand for our good (*ERROR; there is a 20% increase in autonomous demand and not “20% at all price levels”!) but no change in price sensitivity. Q-intercept is now 240….
5. Draw another diag showing that the “sensitivity” of the good has decreased by 50%. In other words, for each $25 increase in price, the Qd decreases by 50% less. (The slope increases.)