Assume the market for fruit from a local fruit stand has the supply and demand c

ID: 1199068 • Letter: A

Question

Assume the market for fruit from a local fruit stand has the supply and demand curves given below.

P = 0.9 - 0.08Q P = 0.1 + 0.02Q

Where P is in dolars and Q is in hundreds of pounds.

Use the information given to graph the market for fruit and indicate each of the following on your graph:

a.) Find equilibrium price and quantity in the market

b.) Calculate consumer surplus at equilibrium

c.) Calculate producer surplus at equilibrium

d.) Determine total economic surplus

e.) Calculate the loss in total economic surplus if a price ceiling is imposed on the market at a price of $0.20

A demand curve is downward sloping, so P = 0.9 - 0.08Q is the demand curve.

Supply curve is upward sloping, so P = 0.1 + 0.02Q is the supply curve.

(a) In equilibrium, demand = supply

0.9 - 0.08Q = 0.1 + 0.02Q

0.1Q = 0.9 - 0.1 = 0.8

Q = 8

P = 0.1 + (0.02 x 8) = 0.1 + 0.16 = 0.26

(b)

From demand curve, When Q = 0, P = 0.9 [Vertical intercept].

So,

Consumer surplus (CS) = Area between demand curve & price = (1/2) x (0.9 - 0.26) x 8 = 2.56

(c)

From supply curve, when Q = 0, P = 0.1 [Vertical intercept]

Producer surplus (PS) = Area between supply curve & price = (1/2) x (0.26 - 0.1) x 8 = 0.64

(d)

Total economic surplus = CS + PS = 2.56 + 0.64 = 3.2

(e) Demand: P = 0.9 - 0.08Q, So 0.08Q = 0.9 - P, or Q = 11.25 - 12.5P

When P = 0.2, demand = 11.25 - (12.5 x 0.2) = 11.25 - 2.5 = 8.75

New CS = (1/2) x (0.9 - 0.2) x 8.75 = 3.06

Supply: P = 0.1 + 0.02Q, or 0.02Q = P - 0.1, Or Q = 50P - 5

When P = 0.2, Supply = 50 x 0.2 - 5 = 10 - 5 = 5

New PS = (1/2) x (0.2 - 0.1) x 5 = 0.25

Total surplus = CS + PS = 3.06 + 0.25 = 3.31

Loss in surplus = 3.31 - 3.2 = 0.11

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