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.
Explanation
(a) Demand and supply shedule
When price = $2, Qd = 30 - 2 =28 Qs = 15 + 2(2) = 19
When price = $4, Qd = 30 - 4 = 26 Qs = 15 + 2(4) = 23
When price = $7 Qd = 30 - 7 = 23 Qs = 15 + 2(7) = 29
| Prices ($) | Quantity demanded | Quantity supplied |
| 2 | 28 | 19 |
| 4 | 26 | 23 |
| 7 | 23 | 29 |
(b)(i) In equilibrium, Qd = Qs
Therefore, 15 + 2p = 3- -p
2p +p = 30 - 15
3p = 15
p = 5
Equilibrium price is $5.00
Substituting for p = 5, we have
Qd = 30 - 5= 25
OR Qs = 15 + 2(5) = 25
(ii) If price is fixed at $3
Qd = 30 - 3 = 27
Qs = 15 + 2(3) = 21
Excess demand is 27 -21 = 6
(c) If the demand function changes to Qd = 40 - p
(i) When price = $2, Qd = 40 - 2 = 38
When price = $4, Qd = 40 - 4 = 36
When price = $7, Qd = 40 - 7 = 33
| Price ($) | Quantity demanded |
| 2 | 38 |
| 4 | 36 |
| 7 | 33 |
(ii) It represents an increase in demand
(iii) At the same prices, more quatities of apples are demanded.