Given the following diagrams: Q_1 = 12 bags. Q_2 = 7 bags. Q_3 = 19 bags. The ma

Question

Given the following diagrams: Q_1 = 12 bags. Q_2 = 7 bags. Q_3 = 19 bags. The market equilibrium price is $46 per bag. The price at point a is $70 per bag. The price at point c is $10 per bag. The price at point d is $56 per bag. The price at point e is $31 per bag. The price at point f is $67 per bag. The price at point g is $32 per bag. Apply the formula for the area of a triangle (Area = 1/2 times Base times Height) to answer the following questions. What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the allocatively efficient output level Q_1 is being produced? $. How large is the dollar value of the consumer surplus at the output level Q_1? $. What is the dollar value of the deadweight loss when output level Q_2 is being produced? $. What is the total surplus when output level Q_2 is being produced? $. What is the dollar value of the deadweight loss when output level Q_3 is produced? $. What is the dollar value of the total s

Explanation / Answer

(a)

Total surplus (TS) = Area of triangle abc

= (1/2) x $(70 - 10) x 12 = (1/2) x $60 x 12 = $360.0

Consumer surplus (CS) = Area between demand curve & market price

= (1/2) x $(70 - 46) x 12 = (1/2) x $24 x 12 = $144.0

(b)

Deadweight loss (DWL) at output Q2 = Area of triangle bed

= (1/2) x $(56 - 31) x (12 - 7) = (1/2) x $25 x 5 = $62.5

TS at Q2 = CS + Producer surplus

= [(1/2) x $(70 - 56) x 7] + [(1/2) x $(31 - 10) x 7] = [(1/2) x $14 x 7] + [(1/2) x $21 x 7]

= $49 + $73.5

= $122.5

(c)

DWL at output Q3 = Area of tringle bgf

= (1/2) x $(67 - 32) x (19 - 12) = (1/2) x $35 x 7 = $122.5

TS at Q3 = [(1/2) x $(70 - 32) x 19] + [(1/2) x $(67 - 10) x 19] = [(1/2) x $38 x 19] + [(1/2) x $57 x 19]

= $361 + $541.5

= $902.5

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