# Subsidies and linear functions (HL)

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Subsidies and linear functions (HL)

Qd = 2,000 – 200P

Qs = -400 + 400P

A subsidy of \$1.50 per unit output is imposed on the product.

Price when quantity supplied is zero:

Qs = -400 + 400P

0 = -400 + 400P

400 = 400P

P = 1

Price when quantity demanded is zero:

Qd = 2000 – 200P

0 = 2000 – 200P

200P = 2000

P = 10

Quantity demanded when price is zero:

Qd = 2000 – 200P

Qd = 2000 – 200(0)

Qd = 2000

Quantity supplied when price is zero:

Qs = -400 + 400P

Qs = -400 + 400(0)

Qs = -400

Equilibrium has shifted from \$4 and 1200 units to \$5 and 1000 units.

Original producer revenue = 1200 * 4 = \$4800

New producer revenue = 1400 * 4.5 = \$6300

Original consumer expenditure = 1200 * 4 = \$4800

New consumer expenditure = 4800 + (200 * 3) =\$5400

Government expenditure = 1400 * 1.50 = \$2100

Original consumer surplus = ((6*12000)/2) =\$3600

New consumer surplus = ((7*1000)/2) =\$3500

Original producer surplus = ((4*12000)/2) =\$2400

New producer surplus = (3*200) + ((3*1000)/2) = \$2100

Original community surplus = 3600 + 2400 =\$6000

New community surplus = 3500 + 2100 = \$4600

Maximum prices

Maximum prices: the government sets a price below the equilibrium price to prevent producers from raising the price above it.

Prices are set in order to protect consumers from the high prices of merit and/or necessary goods because these would be underprovided in a free market.

For instance, during food shortages the government may impose a maximum price on the cost of wheat in order to ensure that food prices a low enough for all income levels to afford. Also in London maximum prices have been used in order to keep the rent lower than the market equilibrium in attempt to ensure affordable accommodation is available for those on low incomes.

When a maximum price at Pmax is put emplace by the government, below the equilibrium price of Pe, there is an excess demand of Qs to Qd. This is because at the new price the quantity demanded is Qd, but the quantity supplied is Qs. S1 is the supply of rented housing at the maximum price in the long run. It gets more elastic as people will stop letting houses as they cannot justify the opportunity cost.

The excess demand from maximum price may result in shortages. This could lead to the emergence of a black market or parallel underground market, where the products are sold at a higher price than the maximum price but less than the equilibrium price.

Non-price rationing systems may emmerge and involve long queues or reservations if working on a first come first serve basis in order to determine which consumers to serve.

Welfare: there is a deadweight loss of BCE. This is because consumer surplus has changed from AEPe to ACBPmax whilst producer surplus has decreased from 0EPe to 0BPmax, as a result of the maximum price imposed. It is therefore not allocative efficient as community surplus is not maximised.

In this diagram, the government has shifted the supply curve from S to S1 by subsidizing, direct provision or using stores to reach the equilibrium at Pmax Qd.

However, these methods can be very expensive and so there is an opportunity cost as the government may have to reduce its expenditure on other industries, like health or education.

Maximum prices and linear functions (HL)

Quantity demanded: 25 units

Quantity supplied: 10 units

Shortage: 15 units

Original consumer expenditure: 6.80 *17 = \$115.60

New consumer expenditure: 10 * 5 = \$50

Additional revenue from selling on the black market: (6.80-5)*17 = \$30.60

Minimum prices

Minimum price: price set above the equilibrium price by the government, which prevents producers from reducing their prices to below it.

Prices are set in order to protect the supply of products that the government believes are important, such as agricultural products. This may be because their products are subject to large price fluctuations or there is a lot of foreign trade. Minimum prices also protect workers as they act as a minimum wage, which ensures that workers earn enough to lead a reasonable existence. Other reasons include for strategic importance and to prevent rural urban migration.

When a minimum price at Pmin is put emplace by the government, above the equilibrium price of Pe, there is an excess supply of Qs to Qd. This is because at the new price the quantity demanded is Qd, but the quantity supplied is Qs.

Minimum prices usually result in a supply surplus. The government may therefore deal with it by increasing demand through advertising, restricting the amount of imports, selling the product cheaply abroad (undermines foreign farmers) or buying the product up themselves and storing or burning it, which can be very expensive. For instance, some EU countries do this and it is referred to as wine lakes and butter mountains.

Other methods to deal with the surplus affect the supply of a product. These are usually quotas which limit how much a producer is legally allowed to produce. The EU calls these method a set aside policy.

Welfare: there is a welfare deadweight loss of BCE. This is because consumer surplus has decreased from AEPe to ACPmin whilst producer surplus has changed from 0EPe to 0ECPmin, as a result of the minimum price imposed. It is therefore not allocative efficient as community surplus is not maximised.

Minimum prices and linear (HL)

Quantity demanded: 23 units

Quantity supplied: 10 units

Surplus: 13 units

Original consumer expenditure: 6.80 *17 = \$115.60

New consumer expenditure: 10 * 8 = \$80

Government expenditure to but surplus: (23-10) * 8 =\$104