Effects of Government Intervention in Markets - Microeconomics

1. A government implements a subsidy for each unit of a good produced. If the demand for this good is perfectly inelastic, what is the effect on the equilibrium price paid by consumers and the quantity sold?
   Answer: Price decreases by the full amount of the subsidy; quantity is unchanged. If demand is perfectly inelastic, the demand curve is a vertical line at a specific quantity. This means consumers will buy that quantity regardless of the price. A subsidy to producers shifts the supply curve down and to the right. To sell the same fixed quantity, suppliers will now be willing to accept a much lower price from consumers, because they also receive the subsidy. The entire benefit of the subsidy is passed on to consumers in the form of a lower price. The consumer price will fall by the full amount of the subsidy. Since demand is perfectly inelastic, the quantity sold remains unchanged.
2. The market for a product is described by demand $Q_d = 2000 - 2P$ and supply $Q_s = P - 100$. The government imposes a price ceiling of $500. What is the maximum price a consumer would be willing to pay on a black market for this product?
   Answer: $800 First, find the equilibrium price to confirm the ceiling is binding: $2000 - 2P = P - 100 \Rightarrow 2100 = 3P \Rightarrow P_e = 700$. Since $500 < $700, the ceiling is binding. At the ceiling price of $500, the quantity supplied to the market is $Q_s = 500 - 100 = 400$ units. The black market price is determined by what consumers are willing to pay for this limited quantity. We find this price by plugging $Q=400$ into the demand equation: $400 = 2000 - 2P_{black} \Rightarrow 2P_{black} = 1600 \Rightarrow P_{black} = 800$.
3. A city government imposes a strict, binding rent control policy. How are the consequences of this policy likely to differ between the short run and the long run?
   Answer: The housing shortage will worsen because both supply and demand become more elastic. In the long run, both the supply of and demand for rental housing are more elastic than in the short run. Supply becomes more elastic because landlords can choose to build fewer new units, convert existing apartments to other uses (like condominiums), or reduce maintenance, effectively decreasing the housing stock. Demand becomes more elastic as people have more time to decide whether to move into or out of the city in response to housing conditions. When both curves become more elastic (flatter), a binding price ceiling will create a much larger gap between the quantity demanded and the quantity supplied. Thus, the shortage will worsen significantly over time.
4. A government wishes to reduce consumption of a good from the equilibrium quantity of 60 units to 40 units. It can achieve this with either a price floor or a per-unit tax. In this market, the demand function is $Q_d = 120 - P$ and the supply function is $Q_s = P$. Which policy would producers prefer, and why?
   Answer: The price floor, because the price they receive would be $80 instead of $40. To reduce quantity to 40, the price consumers pay must be $40 = 120 - P_d \Rightarrow P_d = 80$. The price producers must receive to supply 40 units is $40 = P_s$. A price floor would be set at $80 to achieve the quantity target. Producers would sell 40 units and receive $80 for each. A per-unit tax would require a wedge of $t = P_d - P_s = 80 - 40 = 40$. With the tax, producers would sell 40 units but only receive a net price of $40. Since producer surplus is higher when the price received is $80 compared to $40, producers would prefer the price floor.
5. A government imposes a quota of 80 units in a market, then auctions the quota rights to the highest bidders. If the free market equilibrium would be 120 units at $20, and the demand curve is P = 50 - 0.25Q while supply is P = 5 + 0.125Q, what is the total revenue the government earns from auctioning the quota rights?
   Answer: $800, representing the full quota rent captured by the government through auction With quota of 80 units: Demand price at Q=80: P=50-0.25(80)=$30. Supply price at Q=80: P=5+0.125(80)=$15. Quota rent per unit = $30-$15=$10. Total quota rent = 80×$10=$800. In a competitive auction, quota rights sell for the full quota rent value, as bidders will pay up to the profit margin they can earn. The government captures the entire $800 quota rent. Choice B incorrectly calculates total consumer/producer surplus change. Choice C confuses quota rent with deadweight loss. Choice D assumes government only captures partial rent, which wouldn't occur in efficient auction.
6. The market for a good is defined by $Q_d = 200 - 2P$ and $Q_s = 3P$. The government offers a $10 per-unit subsidy to producers. What is the deadweight loss created by this subsidy?
   Answer: $60 First, find the initial equilibrium: $200 - 2P = 3P \Rightarrow 5P = 200 \Rightarrow P_e = 40$, $Q_e = 120$. A subsidy to producers means the price they receive is $P_p = P_c + 10$. The supply curve becomes a function of $P_c$: $Q_s = 3P_p = 3(P_c + 10) = 3P_c + 30$. Find the new equilibrium by setting this equal to demand: $200 - 2P_c = 3P_c + 30 \Rightarrow 170 = 5P_c \Rightarrow P_c = 34$. The new quantity is $Q_{sub} = 200 - 2(34) = 132$. The deadweight loss (DWL) of a subsidy is the triangle representing inefficient, excess production. Its height is the subsidy amount, and its base is the increase in quantity. DWL = $0.5 \times \text{subsidy} \times (Q_{sub} - Q_e) = 0.5 \times 10 \times (132 - 120) = 0.5 \times 10 \times 12 = 60$.
7. The government imposes a binding price ceiling on a good. Subsequently, the demand for the good becomes significantly more elastic, while the supply curve remains unchanged. What is the effect on the shortage of the good and the deadweight loss (DWL)?
   Answer: The shortage increases, and the DWL increases. A binding price ceiling is set below the equilibrium price. The quantity supplied is $Q_s$ at the ceiling price, and the quantity demanded is $Q_d$. The shortage is $Q_d - Q_s$. When demand becomes more elastic, the demand curve flattens. At the fixed ceiling price, the quantity demanded $Q_d'$ will be greater than the original $Q_d$. Since supply is unchanged, $Q_s$ is constant. Therefore, the new shortage $Q_d' - Q_s$ is larger. Deadweight loss is the loss of surplus from the quantity reduction below equilibrium. Since the quantity traded is fixed at $Q_s$, and the more elastic demand curve is higher than the original demand curve for all quantities less than the original equilibrium quantity, the lost value to consumers is now greater. Thus, the DWL increases.
8. A country restricts imports of a good to a specific quantity. It can do this via a tariff or an import quota where licenses are granted for free to foreign firms. If both policies result in the same domestic price and quantity of imports, which statement is true regarding the importing country's national welfare?
   Answer: National welfare is higher with the tariff because it generates government revenue. Both a tariff and a quota that restrict imports to the same level will raise the domestic price to the same level. The welfare effects on consumers (loss) and domestic producers (gain) are identical. The key difference is what happens to the difference between the world price and the domestic price for the imported units. With a tariff, this difference is collected by the domestic government as tariff revenue, which is part of the national welfare. With a quota where licenses are given to foreign firms, this difference becomes a quota rent captured by those foreign firms, representing a loss of welfare for the importing country. Therefore, national welfare is higher with the tariff.
9. A government introduces a $2 per-unit tax on a good with linear supply and demand curves, causing the equilibrium quantity to fall by 50 units. The government then repeals the tax and introduces a $2 per-unit subsidy on the same good. What will be the new equilibrium quantity under the subsidy?
   Answer: It will be 50 units greater than the original pre-policy equilibrium quantity. For linear supply and demand curves, the change in quantity for a given vertical shift (the wedge) is constant. The tax creates a $2 wedge between the price consumers pay and the price producers receive, causing quantity to fall by 50 units from the original equilibrium $Q_e$ to $Q_e - 50$. A subsidy is a negative tax, creating a $2 wedge in the opposite direction. This will cause quantity to rise by the same amount, 50 units, from the original equilibrium. Therefore, the new quantity will be $Q_e + 50$. Answer choice B is also correct since $Q_e + 50$ is 100 units greater than $Q_e - 50$, but A is a more direct statement about the effect relative to the original equilibrium. Let's re-evaluate. Is one better? A is more precise about the magnitude from the original point. B is about the magnitude from the taxed point. Both are true. Let's re-read the options to find a subtle distinction. Option A says 50 units greater than the original.... This is the most direct application of the symmetry principle. Option B says 100 units greater than the equilibrium quantity that existed under the tax. This is also true: (Qe + 50) - (Qe - 50) = 100. In exams, often there can be two arithmetically correct statements, but one is a better description of the economic event. The effect of the subsidy is an increase of 50 from the baseline. Let's make A the intended answer, as it correctly identifies the magnitude of the change from the no-policy state. Let's assume the prompt wants the change from the initial state. The question is a bit ambiguous. Let's refine the answer choices. Ah, wait, B is (Q_e + 50) - (Q_e - 50) = 100... Both are correct. I need to rephrase. Let me adjust my question or choices. New choice B: It will be 100 units greater than the original pre-policy equilibrium quantity. This would be incorrect. New choice A: It will be 50 units greater than the original pre-policy equilibrium quantity. This is correct. The symmetry of linear curves means a wedge of size X causes the same quantity deviation from equilibrium, regardless of whether it's a tax or subsidy.
10. A government imposes a $10 per-unit tax on the production of a good that generates a marginal external cost of $10 per unit. Before the tax, the market was in a competitive equilibrium. What is the effect of this tax on the total deadweight loss in the market?
    Answer: It eliminates the pre-existing deadweight loss from the externality. In a market with a negative externality, the private market equilibrium quantity is greater than the socially optimal quantity. This divergence creates a deadweight loss. A Pigouvian tax is a tax set equal to the marginal external cost. By imposing this tax, the government forces producers to internalize the externality. The tax raises the private marginal cost of production to equal the social marginal cost. As a result, the market equilibrium quantity decreases to the socially optimal level, and the deadweight loss associated with the overproduction from the externality is eliminated.
11. Consider a market where the government provides a per-unit subsidy to producers. The supply of the good is known to be less elastic than the demand for the good. How will the benefits of the subsidy be distributed?
    Answer: The price producers receive will increase by more than half the subsidy. The incidence of a subsidy, like the incidence of a tax, depends on the relative elasticities of supply and demand. The side of the market that is less elastic (more inelastic) receives a larger share of the benefit. In this case, supply is less elastic than demand. Therefore, producers will capture more of the subsidy's benefit than consumers. This means the price producers receive (net of their costs) will increase by more than the price consumers pay will decrease. Specifically, the increase in the producer price, $P_p - P_e$, will be greater than half the subsidy amount.
12. The government imposes a binding price ceiling on apartment rentals. Under which of the following conditions is this policy most likely to cause a decrease in total consumer surplus?
    Answer: When the supply of apartments is highly elastic and demand is relatively inelastic. Consumer surplus is the area below the demand curve and above the price, out to the quantity consumed. A price ceiling has two effects on consumer surplus: consumers who can still rent an apartment pay a lower price (a gain in surplus), but the quantity of available apartments shrinks, causing some consumers to lose all surplus (a loss). Consumer surplus will decrease if the loss from the quantity reduction is greater than the gain from the price reduction. A highly elastic supply means that a small drop in price (from equilibrium to the ceiling) causes a large reduction in the quantity of apartments supplied. This large quantity reduction magnifies the loss of surplus, making it more likely to outweigh the gains from the lower price, especially if demand is inelastic (meaning consumers placed a very high value on the units that are no longer available).
13. The government imposes a $15 per-unit excise tax on producers in a market with the following demand and supply functions: $$Q_d = 150 - P$$ $$Q_s = 2P$$ What percentage of the total reduction in consumer and producer surplus is captured as government tax revenue?
    Answer: 94.7% First, find the pre-tax equilibrium: $150 - P = 2P \Rightarrow 3P = 150 \Rightarrow P_e = 50$, $Q_e = 100$. The tax on producers shifts the supply curve. Producers' price $P_s$ is what they receive. Consumers' price $P_c$ is what they pay. $P_c = P_s + 15$. The new supply function in terms of $P_c$ is $Q_s = 2(P_c - 15) = 2P_c - 30$. The new equilibrium is $150 - P_c = 2P_c - 30 \Rightarrow 180 = 3P_c \Rightarrow P_c = 60$. The new quantity is $Q_t = 150 - 60 = 90$. The total loss in surplus is the sum of tax revenue and deadweight loss. Tax Revenue = $15 \times 90 = 1350$. Deadweight Loss (DWL) = $0.5 \times \text{tax} \times (Q_e - Q_t) = 0.5 \times 15 \times (100 - 90) = 75$. Total loss in surplus = $1350 + 75 = 1425$. The percentage captured as revenue is $\frac{1350}{1425} \approx 94.7\%$.
14. A government provides a per-unit subsidy to consumers of a good. The supply of the good is upward-sloping and its demand is downward-sloping. Which statement accurately describes the effect on total expenditure on the good?
    Answer: The amount spent by consumers plus the government's subsidy expenditure will equal the new total revenue of producers. After the subsidy, the new quantity is $Q_{sub}$. Consumers pay price $P_c$ and producers receive price $P_p$. The subsidy $s = P_p - P_c$. Consumer expenditure is $P_c \times Q_{sub}$. Government expenditure is $s \times Q_{sub}$. Total expenditure is the sum of these: $P_c Q_{sub} + s Q_{sub} = (P_c + s) Q_{sub}$. Since $P_p = P_c + s$, this simplifies to $P_p \times Q_{sub}$, which is the definition of the new total revenue for producers. Thus, total expenditure on the good (from all sources) equals total revenue for producers.
15. The government imposes a quota limiting the sale of a good to 100 units. Market demand is $Q_d = 500 - 10P$ and market supply is $Q_s = 15P - 250$. What is the total value of the quota rents generated by this policy?
    Answer: $1,667 A quota rent is the economic rent received by the owner of the quota. Per unit, it is the difference between the demand price and the supply price at the quota quantity. First, find the price consumers are willing to pay (the demand price, $P_d$) for 100 units: $100 = 500 - 10P_d \Rightarrow 10P_d = 400 \Rightarrow P_d = 40$. Next, find the price suppliers require (the supply price, $P_s$) to produce 100 units: $100 = 15P_s - 250 \Rightarrow 350 = 15P_s \Rightarrow P_s = 350/15 \approx 23.33$. The quota rent per unit is $P_d - P_s = 40 - 23.33 = 16.67$. The total quota rent is the per-unit rent times the quota quantity: $16.67 \times 100 = 1667$.
16. The government imposes a $3 tax on a good. The price paid by consumers rises by $1. What can be concluded about the relative elasticities of supply and demand?
    Answer: Demand is twice as elastic as supply. The total tax is $3. The consumer's burden is the price increase, which is $1. Therefore, the producer's burden is the remainder of the tax, $\$3 - \$1 = \$2$. The side of the market that is more elastic bears a smaller portion of the tax burden. Since consumers bear $1 and producers bear $2, consumers bear the smaller burden, which means demand is more elastic than supply. The ratio of the burdens is related to the ratio of elasticities. The producer's share is $2/3$ and the consumer's share is $1/3$. The ratio of elasticities (supply elasticity / demand elasticity) is approximately equal to the ratio of burdens (consumer share / producer share). Here, $E_s/E_d \approx (1/3)/(2/3) = 1/2$. This implies that $E_d \approx 2E_s$, meaning demand is twice as elastic as supply.
17. A government removes a binding price ceiling and simultaneously imposes an equivalent per-unit subsidy that results in the same final consumer price as under the price ceiling. Compared to the price ceiling scenario, what happens to producer surplus, consumer surplus, and deadweight loss?
    Answer: Producer surplus increases significantly, consumer surplus remains constant, deadweight loss decreases to zero Under the price ceiling, there was a shortage and deadweight loss. The subsidy that maintains the same consumer price eliminates the shortage by incentivizing producers to supply the full quantity demanded at that price. Consumer surplus remains constant because they face the same price and can now purchase their desired quantity (no more shortage). Producer surplus increases significantly because they receive the consumer price plus the subsidy amount. Deadweight loss becomes zero because the market now clears at the efficient quantity where marginal benefit equals marginal cost. Choice A incorrectly suggests consumer surplus decreases. Choice C incorrectly assumes deadweight loss remains. Choice D overstates consumer surplus gains.
18. The government imposes a binding price floor in a market. Subsequently, it levies a per-unit tax on producers in the same market. What is the most likely effect of adding the tax to the market already constrained by the price floor?
    Answer: The quantity traded will remain the same, but the surplus of the good will decrease. With a binding price floor, the quantity traded is determined by the quantity demanded at that floor price, $Q_d(P_f)$. Adding a tax on producers shifts the supply curve upwards. However, since the price consumers pay is fixed at the floor price $P_f$, the quantity demanded, and therefore the quantity traded, does not change. The surplus of the good is $Q_s - Q_d$. Before the tax, producers supply $Q_s(P_f)$. After the tax, they receive a net price of $P_f - tax$, so they will supply a smaller quantity, $Q_s(P_f - tax)$. Since $Q_d$ is constant and $Q_s$ decreases, the surplus ($Q_s - Q_d$) must decrease.
19. The government imposes a price floor of $50 in a market where demand is $Q_d = 100 - P$ and supply is $Q_s = 2P - 20$. To support this price, the government commits to purchasing any resulting surplus. What is the total cost of this program to the government?
    Answer: $1,500 First, verify the floor is binding. Equilibrium: $100 - P = 2P - 20 \Rightarrow 120 = 3P \Rightarrow P = 40$. The $50 floor is binding. At $P = 50$, quantity demanded is $Q_d = 100 - 50 = 50$. Quantity supplied is $Q_s = 2(50) - 20 = 100 - 20 = 80$. The surplus is $Q_s - Q_d = 80 - 50 = 30$ units. The government purchases this surplus at the floor price of $50. The total cost to the government is $\text{Surplus} \times \text{Price Floor} = 30 \times 50 = 1,500$.
20. A minimum wage is imposed in two low-skilled labor markets, A and B. In Market A, the demand for labor is highly inelastic. In Market B, the demand for labor is highly elastic. In which market will the minimum wage cause a larger increase in unemployment, and in which market will it cause a larger increase in the total income of workers who remain employed?
    Answer: Unemployment increases more in B; income of employed workers increases more in A. Unemployment is the surplus of labor created by the minimum wage, which is the difference between the quantity of labor supplied and demanded at that wage. The more elastic demand is, the more the quantity of labor demanded will fall in response to the wage increase, leading to a larger surplus (unemployment). Thus, unemployment increases more in Market B. The total income of employed workers is the wage rate multiplied by the number of workers employed. Since the minimum wage is the same in both markets, the market with the higher employment will have higher total income for the employed. Because labor demand in Market A is inelastic, the quantity of labor demanded falls by a smaller amount than in Market B. Therefore, employment is higher in A, and the total income of employed workers increases more in A.

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