Question

The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $136. The quantity demanded each month is 1000 when the unit price is $106. The suppliers will market 750 espresso makers when the unit price is $76 or higher. At a unit price of $96, they are willing to market 2250 units. Both the supply and demand equations are known to be linear. (a) Find the demand equation. p = -0.04x + 145 (b) Find the supply equation. p = (x) + 65 x (c) Find the equilibrium quantity and the equilibrium price. 1500 ✓ units $ 85

Answer 1

solution hudreds of dollars. Let R denote the unit poice in Let a be the number of units. demond, curore e a passing through 650, 136) and (1000 , 106). the points The slope of the line m, m = 136 -106 250 - lovo -1125 Then the line equation is, (P-136) = -1 (x-250) P = -1/2 x + 146 Derefore, the demand function is p= 3x+146) (6) The supply curre is a straight line passing through the paint 750,76) (2250, 96) slope of the line Mo - 96-76 2250- 750 T500 = 1175

Then, the line equation is, (P-16) = 1 / (x-750) (P-76) = 2 - 10 P= x - 10+76 p= 4x+66 75 (c) the there fore, the supply equation is (p=1 / 8x + 66 ) To find the equilibrium quantity and price solve equations of demand and supply P = -x + 166 , p = 1 xt 66 75 0 sowe the ean and ege) **]x + 80 =0 (4x+80=0 - 90x75 1 x = 1500 units P= -11 (1500) + 146 -60+146 Ip=86) Rerefore, the equilibrium quantity, is 1500 units and equilibrium price is $86