Question

A group of retailers will buy 80 televisions from a wholesaler if the price is $350 and 120 if the price is $300. The wholesaler is willing to supply 60 televisions if the price is $280 and 140 if the price is $370. Assuming that the supply and demand functions are linear, find the equilibrium point for the market.

What ordered pairs are we given for demand? (don't include units in your answer, one ordered pair per box)

What are our ordered pairs are we given for supply? (don't include units in your answer, one ordered pair per box)

Answer 1

Demands are:

at 350 price demand is 80 units

at 300 price demand is 120 units

If demand is linear then the equation of line will be: Y = MX + C

where,

m is the slope,

y is the price,

x is units,

C is a constant

350 = 80M + C

300 = 120M + C

Solving the above equations, we get

M = -1.25 , C = 450

So the demand curve equation is Price = -1.25*Demand units + 450

Supply are:

60 televisions if the price is 280

140 televisions if the price is 370

If supply is linear then the equation of line will be: Y = MX + C

where,

m is the slope,

y is the price,

x is units,

C is a constant

280 = 60M + C

370 = 140M + C

On solving both the equations, we get

M = 1.125, C = 212.5

So the supply curve is Price = 1.125*Supply units + 212.5

The equilibrium point is where the equation of demand and supply meet i.e. RHS part of both the equation are equal,

=> 1.125*Supply units + 212.5 = -1.25*Demand units + 450

=> Units = 100

Equilibrium price = 1.125*100 + 212.5 = $325

Ordered pairs that are given for demand = 100

Ordered pairs that are given for supply = 100