Question

2. Points = 26. Consider Market Model: Demand: Supply: Q = a -6P Q=-c+dP (a, b>0) (c,d > 0) 1) Discuss in words the meaning of each equation in the model (3 points); 2) Find the equilibrium levels of P and Q (3 points); 3) Draw qualitative conclusions about changes in P and Q' when each of the parameters change. (Qualitative conclusion shows the direction of change.) Explain economic meaning of these changes. (Total 6 points: 3 points for P; 3 points for Q); 4) If a= 10, c = 5, b = 2; d = 3, draw quantitative conclusions about changes in P and Q when each of the parameters change. (Quantitative conclusion shows the magnitude of change.) Explain economic meaning of these changes. (Total 6 points: 3 points for P: 3 points for Q ); 5) Show your conclusions in (4) graphically, Note: Carefully label everything on your graphs. Make the graphs neat and understandable. Points will be deducted for missing labeling and for hard-to- understand graphs. (Total 8 points: 4 graphs -- change in a; change in b; change in c, change in d; -- 2 pts each).

it is all one question, please answer them all! thank you!

Answer 1

1) Demand curve is given by Q=a-bP

Now, when Q=0, P=a/b and when P=0,Q=a. Thus, the demand curve has vertical and horizontal intercepts of a/b and a respectively. -b is the slope of the demand curve (negatively sloped). In the diagram below, we have shown the demand curve.

Again, Supply curve is given by Q=-c+dP

Now, when Q=0, P=c/d and when P=0,Q=-c. Thus, the supply curve has vertical and horizontal intercepts of c/d and -c respectively. d is the slope of the supply curve (positively sloped). In the diagram below, we have shown the supply curve.

Price a/b Supply (a+c)/(b+d) cld Demand (ad-bc)/(b+d) Quantity

2) For equilibrium,

demand = supply

or, a-bP=-c+dP

or, P(d+b)=a+c

or, P = (a+c)/(b+d) is the equilibrium price

and Q = a-bP = a-b{(a+c)/(b+d)} = (ab+ad-ab-bc)/(b+d) = (ad-bc)/(b+d) is the equilibrium quantity

3) When a increases, horizontal and vertical intercepts increases and demand curve shifts to the right. As a result, equilibrium price and quantity rises.

When b increases, vertical intercept falls. As a result, slope of the demand curve becomes flatter. This causes equilibrium price and quantity to fall.

With increase in c, supply curve shifts to the left. Both vertical and horizontal intercept rises. As a result, equilibrium quantity falls but equilibrium price rises.

Now with increase in d, slope of the supply curve becomes flatter (vertical intercept decreases). As a result, equilibrium price falls but equilibrium quantity rises.

4) a=10,b=2,c=5,d=3.

Equilibrium price P=(a+c)/(b+d) = (10+5)/(2+3) = 15/5 = $3

and equilibrium quantity Q = (ad-bc)/(b+d) = (30-10)/(2+3) = 20/5 =4 units

If a increases to 15, P=(a+c)/(b+d) = (15+5)/(2+3)=$4 and Q=(ad-bc)/(b+d) = (45-10)/(2+3)=7 units.

If b increases to 4, P= (a+c)/(b+d) = 15/7 = $2.14 and Q = (ad-bc)/(b+d) = (30-20)/(4+3) = 10/7 = 1.4 units.

If c increases to 8, P=(a+c)/(b+d)=18/5 = $3.6 and Q=(ad-bc)/(b+d) =(30-16)/(2+3)= 2.8 units

If d increases to 5, P=(a+c)/(b+d)= 15/7 = $2.14 and Q=(ad-bc)/(b+d) = (50-10)/(5+3)=40/8 = 5 units.