Find the market equilibrium point for the following demand and supply functions.
Demand: | p | = | −2q + 290 |
Supply: | p | = | 8q + 2 |
(q, p) =
Demand: | 2p | = | −q + 88 |
Supply: | 3p − q | = | 72 |
(q, p) =
Demand: | p | = | −5q + 220 |
Supply: | p | = | 16q + 10 |
1. p = -2q + 290
p = 8q + 2
At equilibrium,
Demand = Supply
-2q + 290 = 8q +2
10q = 290 - 2 = 288
q = 288 / 10 = 28.8 [This is equilibrium q]
p = 8q + 2 = 8(28.8) + 2 = $232.4 [This is equilibrium p]
2. 2p = -q + 88
q = 88 -2p [This is direct demand function]
3p - q = 72
q = 3p - 72 [This is direct supply function]
At equilibrium,
Demand = Supply
88 -2p = 3p - 72
5p = 88 + 72 = 160
p = 160 / 5 = $32 [This is equilibrium p]
q = 88 - 2p = 88 - 2(32) = 24 [This is equilibrium q]
3. p = -5q + 220
p = 16q + 10
At equilibrium,
Demand = Supply
-5q + 220 = 16q + 10
21q = 220 - 10 = 210
q = 210 / 21 = 10 [This is equilibrium q]
p = 16q + 10 = 16(10) + 10 = $170 [This is equilibrium p]
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