Question

2. Let the demand and supply functions be as follows: (a) Qd-51 – 3P (6) Qd = 30 – 2P Qs = 6P - 10 Qs = -6 +5P find P* and Q* by elimination of variables. (Use fractions rather than decimals.) 3. According to (3.5), for Q* to be positive, it is necessary that the expression (ad – bc) have the same algebraic sign as (b+d). Verify that this condition is indeed satisfied in the models of Probs. 1 and 2. 4. if (b+d)= 0 in the linear market.model, can an equilibrium solution be found by using (3.4) and (3.5)? Why or why not? 5. If (b+d) = 0 in the linear market model, what can you conclude regarding the posi- tions of the demand and supply curves in Fig. 3.17 What can you conclude, then, regarding the equilibrium solution?

Answer 1

1. P* and Q* are the equilibrium price and Quantity respectively. Equilibrium occurs at the point where demand and supply curve intersects. At this point, Qd = Qs

2. a) Qd = 51-3P and Qs = 6P-10 Equilibrium occurs where Qd = Qs : 51-3P = 6P-10 * 9p=61 PEG! - 67 At this price from any of demand or supply equation We get, Qd = Qs = 92 - 30 7 2 = G* Equilibrium price (pt) = 6 7 and equilibrium Guantity (Q*) = 30 31 Qd = 30-2P Gs=-6+5P At equilibrium Gd = Gs. - 30-2P = -6+5P » 7P=36 * P * = 36 = 5 2 - 1 At pt = 36 from any of demand as supply equation I we get, Qd = Qs = 138 = 19 5 5 = 6* p*= 5 7 and G* = 19 / 12

Answer 2

P=61/9 and Qd=92/3