Question

A group of retailers will buy 92 televisions from a wholesaler if the price is $475 and 132 if the price is $425. The wholesaler is willing to supply 56 if the price is $425 and 136 if the price is $515. Assuming that the resulting supply and demand functions are linear, find the equilibrium point for the market.

Answer 1

Let (P, Q) be the equilibrium point for the market.

For Demand,

(475, 92) -> (P1, Q1)

(425, 132) -> (P2, Q2)

(P - P1) / (P2 - P1) = (Q - Q1) / (Q2 - Q1)

(P - 475) / (425 - 475) = (Q - 92) / (132 - 92)

(P - 475) / -50 = (Q - 92) / 60

6(P - 475) = -5(Q - 92)

6P - 2850 = -5Q + 460

6P + 5Q = 3310 ---(1)

For Supply,

(425, 56) -> (P1, Q1)

(515, 136) -> (P2, Q2)

(P - P1) / (P2 - P1) = (Q - Q1) / (Q2 - Q1)

(P - 425) / (515 - 425) = (Q - 56) / (136 - 56)

(P - 425) / 90 = (Q - 56) / 80

8(P - 425) = 9(Q - 56)

8P - 3400 = 9Q - 504

8P - 9Q = 2896 ---(2)

Multiply equation (1) by 4 and equation (2) by 3 and subtracting both we get,

4(6P + 5Q - 3310) - 3(8P - 9Q - 2896) = 0

24P + 20Q - 13240 - 24P + 27Q + 8688 = 0

47Q = 4552

Q = 96.85

Now from (1),  6P + 5Q = 3310

6P + 5 * 96.85 = 3310

6P = 2728.9

P = 454.82

Thus, the equilibrium point for the market is (454.82 , 96.85)