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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.

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Answer:

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

Solving equation 1 and 2 together we get,  [tex]30 = 750b

=b = 0.042 [/tex]

Substituting this value for b into equation 1 we get,

[tex]135 = a – 0.042(250)

135 = a – 10.667

145.667 = a  [/tex]

Substituting a and b into the demand equation we have,

Demand equation= [tex]P = 145.67 – 0.04Q

Qd= 1/0.04 (145.67 – P) [/tex]

Similarly,

Supply equation is given by P= c + dQ  

[tex]Equation 3 = 72 = c + d700

equation 4 = 102 = c +d 2200

Solving equation 3 and 4 together we have, 30 = 1500d

d =0.02

Substituting value for d into equation 3 we have,

72 = c + 0.02(700)

72 = c +14

c=58

Putting c and d into the Supply equation we get,  P= 58 + 0.02Q [/tex]

[tex] Qs= 1/0.02 (P – 58)

In equilibrium, demand is equal to supply

Qd= Qs

1/0.02 (P – 58) = 1/0.04 (145.67 – P)

2(P -58) = 145.67 – P

2P – 116 = 145.67 – P

P = $29.67  - Equilibrium price

Substituting this into the demand equation we have,

P = 145.67 – 0.04Q

29.67 = 145.67 – 0.04Q

Q= 145.67 – 29.67/0.04

Q = 116/0.04

Q= 2900  = Equilibrium quantity[/tex]


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