In: Economics
When the price is $30 per unit, buyers in a market are willing to buy 400 gadgets and when the price is $60 per unit, they are only willing to buy 100 gadgets. When the price is $30 per unit, sellers in a market are only willing to sell 150 gadgets and when the price is $60 per unit, they are willing to sell 225 gadgets. Assume (1) the economic environment of buyers (their income, tastes or preferences, other prices, and expectations) and sellers (technology, input prices, etc.) are constant and (2) the demand and supply curves are linear all along. What price in this market would make the quantity demanded equal to 200 units?
SOL;
Equation for demand function will be
P - 30 = [60 -30]/[100- 400] [Q - 400]
P - 30 = -1/10 [Q - 400]
P = 70 - Q/10
IF Q = 200
P = 50
Equation for supply function
P - 30 = [60 - 30]/ [225 - 150] [Q - 150]
P - 30 = 2/5 [Q - 150]
P = 2/5 Q - 30
IF Q = 200
P = 50
So at price of 50 demand will equal 200 and market will be in equilibrium.