12.9: Problem Sets
- Page ID
- 308974
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Why can price ceilings create shortages?
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A price ceiling sets a maximum legal price that sellers can charge. It is designed to keep essential goods more affordable for consumers, particularly during times of scarcity or price spikes — for example, capping food prices during emergencies to prevent price gouging. When set below equilibrium, it lowers prices for consumers but can create shortages because producers are less willing to supply the product at the lower price.
Why can price ceilings create shortages?
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A binding price ceiling (below equilibrium) increases quantity demanded but reduces quantity supplied. Since buyers want more at the lower price and producers provide less due to reduced profitability, quantity demanded exceeds quantity supplied. The result: a shortage — often accompanied by rationing, long lines, or black markets.
What is the primary objective of a price support? Who benefits?
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A price support sets a minimum legal price — typically above equilibrium — to help producers earn a higher, more stable income. In agriculture, governments use price supports to protect farmers from volatile markets and low prices. Producers benefit because they receive a guaranteed higher price; however, consumers face higher prices and reduced quantity demanded.
What happens when the government purchases surplus under a price support?
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If a price support causes surplus production, the government may buy the excess. This keeps prices artificially high, ensuring producer income, but taxpayers bear the cost of purchasing and storing or disposing of surplus. Consumers lose (pay higher prices), producers gain (sell at a high guaranteed price), and society experiences deadweight loss due to inefficiency.
How does a quantitative output restriction affect price and quantity?
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A quantitative restriction limits the amount producers can supply. This reduced supply raises market price. Producers may gain if demand is inelastic (consumers still buy despite higher prices), but if demand is elastic, producers could lose revenue. No physical surplus occurs, but consumers pay more and buy less, creating deadweight loss.
What is an import quota and why is it used?
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An import quota limits how much of a foreign good can enter a country. It is typically used to protect domestic industries — like sugar producers — from lower-cost international competition. By restricting imports, domestic prices rise, benefiting producers who can now sell at higher prices.
Who gains and who loses from an import quota?
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Gainers: Domestic producers (higher prices and production) and the government (quota revenue from selling import permits).
Losers: Consumers (pay higher prices and consume less).
Because resources shift to less efficient producers, there is deadweight loss — society is worse off overall.
What is the difference between a specific tax and an ad-valorem tax?
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Specific tax: A fixed amount per unit sold (e.g., $0.50 per gallon of gas).
Ad-valorem tax: A percentage of the product’s price (e.g., 8% sales tax).
Both raise buyer prices and reduce seller revenue, but ad-valorem taxes increase with price changes.
Who pays a tax — buyers or sellers?
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The burden (tax incidence) is shared by buyers and sellers depending on elasticity. The tax creates a wedge between consumer and producer prices.
If demand is inelastic, consumers bear more of the tax.
If supply is inelastic, producers bear more.
How do subsidies affect consumers, producers, and taxpayers?
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Subsidies lower the price consumers pay and raise the price producers receive.
Consumers benefit (lower prices)
Producers benefit (higher revenue and output)
Although both consumers and producers gain, society incurs a deadweight loss because government spending exceeds the value created.
Taxpayers fund the subsidy, creating a government cost