Term 2 Week 4: Price Controls, Tariffs and Quotas, Taxation and Subsidies Flashcards
What are 3 applications of the demand and supply model (3)
-Price controls
-Tariffs and quotas
-Taxes and subsidies
How to graphically represent a maximum price being added (4)
-Imagine a demand and supply diagram in equilibrium
-Add P max below the market equilibrium price
-This causes there to be a gap between Qd and Qs
-The new consumer surplus is under the demand curve, above the max price and to the left of Qs
What are things to consider with max/min prices (2)
-The minimum/maximum price needs to be above/below market equilibrium to have an impact
-The price control could impact not only quantity but quality of supply, as producers with lower prices have less of an incentive to maintain quality, amidst lower profits
What do we have to consider with a minimum wage (3,2)
When implementing a minimum wage, we have to consider:
-Is the minimum wage a binding constraint in all markets
-What is the short run vs long run impact
-Is there change along the intensive (paid more) or extensive (less hired) margin
-The estimated elasticity is -0.1, where a 10% rise in the minimum wage leads to a 1% fall in employment
-The more elastic labour demand is, the larger the rise in unemployment to a change in minimum wage (higher ease of automation)
How can intervention in markets have different effects on surplus (3)
-The conversion of CS to PS, or PS to CS
-The conversion of CS or PS to Tax revenue
-The creation of deadweight loss (any surplus lost relative to the most efficient outcome)
How to draw a diagram showing a less efficient country vs a world price (4)
-Start off with quantity on the x axis, price on the y axis, and a normal Qs and Qd diagram, with p* and q*
-The world price is below equilibrium, as the country is smaller and less specialised/efficient
-The new supply is now the normal until the world price, and perfectly elastic after (still draw the full upwards supply curve)
-This leads to a v small producer surplus (the area under Pw_, a very large consumer surplus (Area under demand above Pw) and total imports of (pw x (QwD - QwS))
How to represent the addition of a tariff diagramatically (5)
-Start off with the diagram showing an inefficient country vs world price
-Shift the world price upwards from pw to p(w+t)
-Producer surplus rises to the area above the supply curve and below p(w+t)
-There is now tariff revenue of the rectangle of new difference between Qd and Qs, and t (p(w+t) - pw)
-There is deadweight loss in the 2 little triangles to the left and right of the tariff revenue, trapped by the 2 prices and D/S curves
What is the impact of tariffs on different agents (4)
-Increased producer surplus
-Governments gain increased tax revenue
-Decreased consumer surplus
-Deadweight loss
What are quotas, and how can they be graphically represented (1,2,4)
-Quotas place restrictions on the quantity of imported goods, and can be implemented through government auction of licences, country allocations or proportions of important licenses
-Imagine a demand and supply diagram
-The quota (x) leads to the supply curve being perfectly elastic at the world price, before the domestic producers continue to produce
-CS remains the same, area above p* below D curve
-PS is now the area above Qs below p* but not the perfectly elastic area
-The perfectly elastic area is Quota rent (above S, below p), either government revenue if quotas auctioned or foreign producer surplus if goods sold at p
-DWL occurs between the triangle under Qs and Qd, and above Pw
What are the similarities/differences between Tariffs and quotas (2,1)
-Tariffs and quotas achieve the same objective in raising domestic prices, and supporting domestic producers
-When comparing the 2, consumer and domestic producer surplus is identical
-Quotas are no better than tariffs, but can be worse if revenue is not collected
What do taxes do (2)
-When a tax is imposed, the market will adjust so that it is in equilibrium
-A tax will drive a wedge between final price payed per buyer and price received by suppliers
What are the impact of per unit taxes (1,4)
-Per unit taxes have fixed nominal value t charged on every unit sold
-When certain value t is added to equilibrium price, this will cause a decrease in supply from Q* to Q** (Q** = demand at the higher price)
-Consumer burden is the rectangle between PD and the equilibrium price to the left of Q**
-Producer burden is the area above Ps (supply price at Q), below equilibrium price and to the left of Q
-Deadweight loss is the triangle to the right of tax burden, above Qs and below Qd
How does DWL change depending on Q (1)
-The less Q changes, the less DWL there is, as more lost surplus is converted to tax revenue
How to illustrate the impact of a subsidy (2,4)
-Imagine a classic demand and supply diagram
-The subsidy (Ps - Pd) leads Q* to rise to Q**, with a higher Ps and lower Pd
-The government spending on the subsidy is (Ps - Pd)(Q)
-The new consumer surplus is the area below D, above Pd and to the left of Q
-The new PS is the area above QS, below Ps and to the left of Q**
-Lost surplus is thus the triangle not covered by either of these surpluses in the spending (government spending not regained by rises in PS or CS)
How to mathematically work out DWL (4 (original p and q), 4(new p and q), 4 (dwl and for P and C)
-Assume linear demand, so that Qd = a-bp, and QS = c + dp
-a-bp = c + dp
-p* = (a-c)/(b+d)
-Q* = c + d((a-c)/(b+d))
-After the tax is imposed, Qd(pd) = Qs(ps)
-a-b(ps+t) = c+d(ps)
-ps = (a-c-bt)/(b+d)
-Q** = c + d((a-c-bt)/(b+d))
-∆Q = Q* - Q** = ((bd)/(b+d))t
-DWL = 0.5t∆Q = 0.5((bd)/(b+d))t^2
-For producers: 0.5(bdt)/(b+d)(p-ps) =0.5(b^2d)/(b+d)^2)t
-For consumers: 0.5(bdt)/(b+d)(pd-p) =0.5(bd^2)/(b+d)^2)t
What is the DWL function (3)
-DWL = 0.5t∆Q = 0.5((bd)/(b+d))t^2
-For producers: 0.5(bdt)/(b+d)(p-ps) =0.5(b^2d)/(b+d)^2)t
-For consumers: 0.5(bdt)/(b+d)(pd-p) =0.5(bd^2)/(b+d)^2)t
What can we tell from the DWL function (1,2)
-DWL is zero either when b (PED) or d (PES) is 0
-t^2 shows how marginal cost (DWL) is increasing at an increasing rate
-We thus want to spread tax across different markets as it is a convex function
How do we mathematically derive the optimal tax rate (2,4,1)
-min ∑DWL(t) s.t. ∑tQ**(t) = R
-We’re trying to minimise the cost to society subject to the minimum revenue made after tax
L = ∑ 0.5((bd)/(b+d))t^2 - λ(∑t[c + d((a-c-bt)/(b+d)))] - R (set up a lagrangian minimising tax subject to revenue)
-∂L/∂t = (bd)/(b+d)t - λ(Q-t(bd)/(b+d)) = 0
-t(bd)/(b+d)(1+λ) = λQ
-t = (λ/(1+λ))((b+d)/(bd))Q**
-λ can be thought as the marginal DWL of government spending, the lagrange multiplier attached to the revenue constraint
What is the expression for the optimal tax rate (1)
t = (λ/(1+λ))((bd)/(b+d))Q**
How can we compare optimal tax rates across markets (3)
-When comparing across markets, we must normalise relative to the price of the good
-b and d are relative to the slopes of Qd and Qs, but slopes are measured in different units for different goods
-We can normalise using % taxes (τ) and elasticities (ad valorem taxes)
What is the Ramsey rule
τ ≈ 1/|εs| + 1/εd|
How can we mathematically derive the Ramsey rule for optimal tax (2,3,2,1)
-The optimal tax rule = (λ/(1+λ))((bd)/(b+d))Q**
-Let λ/(1+λ) = k
-Divide by Ps on both sides:
-τ = k((b+d)/(bd))(Q/Ps)
-For a small tax where Q ≈ Q and P ≈ Ps, τ ≈ k((b+d)/(bd))(Q/P)
-By multiplying by p/q twice on the top and bottom, we can restate as: τ ≈ k((bP/q)+(dP/q)/(bP/Q)d(P/Q)) (P/Q)(Q/P)
-or τ ≈ k (|εD| + |εs|)/(|εd||εs|) (remeber b is PED, d PES, so we can convert them to elasticities though multiplying by P/Q
-τ ≈ k(1/|εs| + 1/εd|)
What can we infer from Ramseys optimal tax rule (1, 3)
-The ramsey rule shows us optimal tax rates are higher when demand and supply are more inelastic
-This is because DWL is caused by changes in Q
-Q for inelastic markets doesn’t change much with price
-Taxes on inelastic products have less distortionary effects
