Question

The quantity demanded x each month of russo espresso makers is 250 when the unit price p is $135. the quantity demanded each month is 1000 when the unit price is $105. the suppliers will market 700 espresso makers when the unit price is $72. at a unit price of $102, they are willing to market 2200 units. both the supply and demand equations are known to be linear.

Answer 1

`Demand equation is given by, P =a –bQ   Equation 1 = 135 = a – b 250  Equation 2 = 105 = a -  b 1000`

Solving equation 1 and 2 together we get,
`30 = 750b</p><p>=b = 0.042`

Substituting this value for b into equation 1 we get,

`135 = a – 0.042(250) </p><p>135 = a – 10.667 </p><p>145.667 = a`

Substituting a and b into the demand equation we have,

Demand equation=
`P = 145.67 – 0.04Q </p><p>Qd= 1/0.04 (145.67 – P)`

Similarly,

Supply equation is given by P= c + dQ

`Equation 3 = 72 = c + d700 </p><p>equation 4 = 102 = c +d 2200 </p><p>Solving equation 3 and 4 together we have, 30 = 1500d </p><p>d =0.02 </p><p>Substituting value for d into equation 3 we have, </p><p>72 = c + 0.02(700) </p><p>72 = c +14 </p><p>c=58 </p><p>Putting c and d into the Supply equation we get,  P= 58 + 0.02Q`

`Qs= 1/0.02 (P – 58) </p><p>In equilibrium, demand is equal to supply </p><p>Qd= Qs</p><p>1/0.02 (P – 58) = 1/0.04 (145.67 – P) </p><p>2(P -58) = 145.67 – P </p><p>2P – 116 = 145.67 – P </p><p>P = $29.67  - Equilibrium price </p><p> Substituting this into the demand equation we have, </p><p>P = 145.67 – 0.04Q </p><p>29.67 = 145.67 – 0.04Q </p><p>Q= 145.67 – 29.67/0.04 </p><p>Q = 116/0.04 </p><p>Q= 2900  = Equilibrium quantity`