Consider the demand function for processed pork in Canada, Qd-546 00-19p + 20pb
ID: 1135045 • Letter: C
Question
Consider the demand function for processed pork in Canada, Qd-546 00-19p + 20pb + 3pc +0002Y The supply function for processed pork in Canada is: a,#354 00 . 47p-60pm Po is the price of beef $4 per kg Pc is the price of chicken $3 per kg Y is the income of consumers $12,500 Ph is the price of a hog $1.50 per kg p is the price of pork Q is the quantity of pork demanded (measured in millions of kg per year) Solve for the equilibrium price and quantity for pork. The equilibrium price of pork is Sand the equilibrium quantity of pork is million kg per year. (Enter numeric responses using real numbers rounded up to two decimal places.)Explanation / Answer
Answer : Given,
Demand : Qd = 546 - 19P + 20Pb + 3Pc + 0.002Y
By putting all given values in demand function we get,
Qd = 546 - 19P + (20 × 4) + (3 × 3) + (0.002 × 12,500)
=> Qd = 546 - 19P + 80 + 9 + 25
=> Qd = 660 - 19P
=> 19P = 660 - Qd
=> P = (660 - Qd)/19
=> P = 34.74 - 0.05Qd .......... (i)
Given, supply : Qs = 354 + 47P - 60Ph
By putting given values in supply function we have,
Qs = 354 + 47P - (60 × 1.50)
=> Qs = 354 + 47P - 90
=> Qs = 264 + 47P
=> Qs - 264 = 47P
=> P = (Qs - 274)/47
=> P = 0.02Qs - 5.83 ........ (ii)
Now, at equilibrium condition, Demand = Supply.
=> 34.74 - 0.05Qd = 0.02Qs - 5.83
=> 34.74 + 5.83 = 0.02Qs + 0.05Qd
[As Qs = Qd = Q at equilibrium]
=> 40.57 = 0.02Q + 0.05Q
=> 40.57 = 0.07Q
=> Q = 40.57 / 0.07
=> Q = 579.57
Now by submitting Q = 579.57 in equation (i) we have,
P = 34.74 - (0.05 × 579.57)
=> P = 34.74 - 28.98
=> P = 5.76
Therefore, P = $5.76 is equilibrium price level and Q = 579.57 millions kg per year is equilibrium quantity level for pork.