P = 10 – 0.2 Qd, Reports Examples
Assume that demand for a commodity is represented by the equation P = 10 – 0.2 Qd, and supply by the equation P = 2 + 0.2 Qs where Qd and Q s are quantity demanded and quantity supplied, respectively, and P is the Price. Use the equilibrium condition Qs = Qd ,
1: Solve the equations to determine equilibrium price.
The equilibrium price (P) is the price at which the quantity supplied (Qs) equals the quantity demanded (Qd) and can be represented in the equilibrium condition Qs=Qd. From the above mentioned equations we have:
0.2Qd = 10-P,
Qd = 50-5 P; (1)
and P = 2 + 0.2 Qs,
P-2 = 0.2 Qs,
Qs = 5 P – 10; (2)
Thus, to find the equilibrium price we have to solve the equation Qs (2) = Qd (1)
5 P - 10 = 50 – 5 P,
10 P = 60,
P = 6; (3)
The equilibrium price of the commodity analyzed in this case is 6.
2: Now determine equilibrium quantity.
There are several ways to determine the equilibrium quantity. The first one is to solve the equation 10 – 0.2 Qd = 2 + 0.2 Qs assuming that Qs=Qd=Q, as the price (P) is the same. Thus, the equation will look as follows:
10 – 2 = 0.2Q + 0.2 Q,
0.4 Q = 8,
Q = 20; (4)
The other way is to substitute P for the found meaning of the equilibrium price (‘6’).
6=10-0.2 Qd,6=2+0.2 Qs;
0.2 Qd=4,0.2 Qs=4;
Qs = Qd =20; (5)
So, for the price P = 6 consumers will buy and producers will make the commodity in quantity of Q = 20.
3: Graph the two equations to substantiate your answers and label these two graphs as D1 and S1.
The other way to determine equilibrium price either equilibrium quantity is to find an intersect of demand and supply curves (D1 and S1). As it is shown on the graph below, the point of intersection reflects the equilibrium price (P = 6) measured before, as well as the equilibrium quantity, achievable at this price (Q = 20).
Figure 1. Supply and demand intersect.
4: Furthermore; assume the demand for this product increases because of a change in income.
A: graph the new demand curve and label as D 2.
As it is represented on the graph 2, once the income increases the demand on the commodity will increase as well.
Figure 2. Supply and demand intersect in case the demand increases.
B: What will be the new equilibrium price and quantity compare to the initial one.
The curve D2 shows the increased demand level. Since this curve moved up, the equilibrium price as well as the equilibrium quantity increased as well. To measure new meanings of these characteristics, we should first find the new point of intersection. It will lead us to the new price Pe* and quantity Qe*. Thus it is clear that Pe* is higher than the previous P = 6, as well as Qe* is higher than Q = 20.
C. Is this product normal good or inferior good?
As it was stated previously, after income level increased the demand for this good has increased as well. Therefore, the analyzed commodity is a normal good. Inferior goods have an opposite result to the income growth. Usually, when the average welfare level increases the demand for inferior goods drops down. Among the inferior goods there are inexpensive goods like cheap cars, frozen food, stock clothes etc. So, once people start earn more they prefer to consume goods of higher quality.
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