The market for apples is represented by the following demand and supply functions:
Qd = 30 - p;
Qs = 15 + 2p.
(a) Prepare a demand and supply schedule for the market, given the prices $2.00, $4.00 and $7.00.
(b) (i) Determine the equilibrium price and equilibrium quantity of apples in the market.
(ii) If the price of apple is fixed at $3.00, what will be the excess demand or excess supply.
(c) Suppose the demand function changed to Qd = 40 - p. Using the prices in (a) above:
(i) prepare a new demand schedule;
(ii) does it represent an increase or a decrease in demand?
(iii) explain your answer in (c) (ii) above.
(a) Demand and supply schedule using \( Q_d = 30 - p \) and \( Q_s = 15 + 2p \).
| Price (\$) | Quantity demanded (Qd) | Quantity supplied (Qs) |
|---|
| 2.00 | 28 | 19 |
| 4.00 | 26 | 23 |
| 7.00 | 23 | 29 |
(b)(i) Equilibrium. Equilibrium is where \( Q_d = Q_s \):
\[ 30 - p = 15 + 2p \Rightarrow 15 = 3p \Rightarrow p = 5 \]
Equilibrium quantity: \( Q = 30 - 5 = 25 \). So equilibrium price = \$5.00 and equilibrium quantity = 25 units.
(b)(ii) At a fixed price of \$3.00: \( Q_d = 30 - 3 = 27 \); \( Q_s = 15 + 2(3) = 21 \). Since quantity demanded exceeds quantity supplied, there is excess demand of \( 27 - 21 = 6 \) units (a shortage), which is expected because \$3.00 is below the equilibrium price.
(c)(i) New demand schedule with \( Q_d = 40 - p \):
| Price (\$) | New quantity demanded |
|---|
| 2.00 | 38 |
| 4.00 | 36 |
| 7.00 | 33 |
(c)(ii) It represents an increase in demand.
(c)(iii) Explanation. At every price the quantity demanded is now higher than before (for example at \$2.00 it rises from 28 to 38). This means the whole demand curve has shifted to the right, which is the definition of an increase in demand. It is caused by a change in a non-price determinant such as a rise in consumers' income, a change in taste in favour of apples, or a rise in the price of a substitute.
