Question

1) Consider a demand curve of the form Qd = 20-2p where Qd is the quantity demanded of a good and p is the price of the good. Also consider a supply curve of the form Qs = 2p-4 where Qs is the quantity supplied. Graph these curves. At what values of P and Q do these curves intersect?

2) Now suppose at each price individuals demand four more units of output, that is the demand curve shifts to Qdd = 24-2p. Graph this new curves. Graph this new curve on the diagram drawn in part 1) At what values of P and Q does the new demand curve intersect the supply curve identified in part 1)

Answer 1

1.

The given demand curve is $Qd = 20−2p$

and the supply curve is  $Qs = 2p−4$

At equilibrium

$Qd = Qs\\ => 20−2p = 2p − 4\\ => 20+4 = 4p\\ => p =244= 6\\ Then\\Qd = 20−2p\\ =20 − 2×6=8\\$

For different values of p=[3,4,5,6,7], the quantity was calculated to plot the graph. The graph intersects at price $6 and quantity 8 units.

2)The new demand curve is  $Qd = 24−2p$

the equilibrium price and quantity will change.

At the new equilibrium

$Qd = Qs\\ =>24−2p=2p−4\\=>24+4 = 2p +2p\\=> 28 = 4p\\=> p =7 Thus, \\ Qd = 24−2p \\ =24−2×7\\ =24−14 \\ =10$

The green line is the new demand curve. The graph is plotted by taking the same values of price as earlier, p=[3,4,5,6,7]. The graph intersects at price $7 and quantity 10 units.