Economics

David Begg, Gianluigi Vernasca, Stanley Fische

Chapter 4

Elasticities of demand and supply - all with Video Answers

Educators

Chapter Questions

Problem 1

Your fruit stall has 100 ripe peaches that must be sold at once. Your supply curve for peaches is vertical. From past experience, 100 peaches are demanded if the price is $£ 1$. The demand elasticity is $-0.5$. (a) Draw a supply and demand diagram showing market equilibrium. (b) You discover 10 of your peaches are rotten and cannot be sold. Draw the new supply curve. What is the new equilibrium price?

Andrew Davis

Andrew Davis

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Problem 2

For each of categories (a), (b) and (c), do you expect demand to be elastic or inelastic? (a) Milk, dental services, beer; (b) chocolate, chicken, train journeys; (c) theatre trips, tennis clubs, films. Then rank the elasticities within each category. Explain your answers.

Khalida Dawar

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Problem 3

Where along a straight-line demand curve does consumer spending reach a
maximum? Explain why. What use is this information to the owner of a football club?

Khalida Dawar

Numerade Educator

Problem 4

The following table shows price and income elasticities for vegetables and catering services. For each good, explain whether it is a luxury or a necessity, and whether demand is elastic or inelastic.

Emily Himsel

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Problem 5

Common fallacies Why are these statements wrong? (a) Because cigarettes are a necessity, tax revenues from cigarettes will always increase when the tax rate is raised. (b) Farmers should take out insurance against bad weather that might destroy half of all their crops. (c) Higher consumer incomes always benefit producers.

Khalida Dawar

Numerade Educator

Problem 6

The data below refer to the market for cheese:
$$
\begin{array}{|l|l|}
\hline \text { Quantity } & \text { Price } \\
\hline 130 & 10 \\
\hline 110 & 20 \\
\hline 80 & 35 \\
\hline 70 & 40 \\
\hline 58 & 46 \\
\hline 50 & 50 \\
\hline
\end{array}
$$
Plot the demand for cheese. Given that the demand for cheese is unit elastic at $37 \mathrm{p}$, for which prices is the demand for cheese elastic? For which ones is the demand for cheese inelastic?

Khalida Dawar

Numerade Educator

Problem 7

Consider the following demand function: $Q^{D}=25 / \mathrm{P}^{2}$. Show that the point elasticity of demand for that function is always equal to $-2$.

Khalida Dawar

Numerade Educator

Problem 8

The data below refers to the quantity demanded of good $\mathrm{A}$ and the price of $\mathrm{A}$ as a result of changes to the price of good $\mathrm{B}$ and good $\mathrm{C}$ :
$$
\begin{array}{|l|l|l|l|}
\hline Q_{A}(\mathrm{~kg}) & P_{A} \text { (pence) } & P_{B} \text { (pence) } & \left.P_{C} \text { (pence }\right) \\
\hline 3 & 52 & 32 & 64 \\
\hline 1.3 & 82 & 26 & 71 \\
\hline
\end{array}
$$$$
\text { Are goods A and B substitutes or complements? What about goods A and C? }
$$

Khalida Dawar

Numerade Educator

Problem 9

Air conditioners are a luxury good. (a) What does this imply about income elasticity? (b) Which two countries would you guess have the highest per capita demand for air conditioners at present? (c) If people continue to get richer and global warming continues to increase, what is likely to happen to the quantity of air conditioners demanded? And what will this do to global warming? And hence to the demand for air conditioners? (d) Could this process spiral out of control?

Khalida Dawar

Numerade Educator

Problem 10

Suppose the government levies a tax of $55 \mathrm{p}$ per bottle of wine. Show on a graph the effect of this tax on the equilibrium price and quantity assuming that the demand for wine is elastic. Do consumers or suppliers bear a greater proportion of the tax?

Khalida Dawar

Numerade Educator

Problem 11

(a) If the government wants to maximize revenue from cigarette tax, should it simply set a very high tax rate on cigarettes? (b) If the government achieves its objective, what is the elasticity of demand for cigarettes at the price corresponding to this tax rate? You may assume that cigarettes are essentially free to produce and the entire price reflects the tax. (c) A research company measures elasticity and concludes that the demand for cigarettes is price-elastic. Should the government raise or lower the tax rate? (d) If the government wants to get some tax revenue but also wants to make people smoke less, should it set a tax rate above or below that which maximizes revenue from cigarette taxation?

Khalida Dawar

Numerade Educator

Problem 12

Essay question Suppose climate change causes flooding that wipes out much of UK agriculture. Discuss what happens to the price of food in the UK: (a) in the short run and (b) in the long run. Did you assume that the UK made and consumed all food itself or did you allow for international trade? How does the outcome differ in these two cases?

Khalida Dawar

Numerade Educator

Problem 13

Suppose that the market demand for beef is given by $Q^{D}=200-6 P+2 Y$, where $P$ is the price of meat per $\mathrm{kg}$ and $Y$ is the consumers' income. Suppose that consumers' income is $£ 100$. If the price of beef decreases from $£ 10$ to $£ 8$ per $\mathrm{kg}$, find the corresponding elasticity of demand. Now suppose that the price is fixed to $£ 8$ while consumers' income increases from $£ 100$ to $£ 150$; find the corresponding income elasticity of demand. Is beef a normal good?

Khalida Dawar

Numerade Educator

Problem 14

The market demand for a given good is $Q^{D}=26-4 \mathrm{P}$, while the market supply is $Q^{S}$ $=2 \mathrm{P}-4$. Find the equilibrium price and quantity in the market. Now assume that the government introduces a specific tax $t=3$ on the suppliers. Find the new equilibrium price and the new equilibrium quantity. Compare the pre-tax equilibrium with the after-tax equilibrium. What are the main differences?

Khalida Dawar

Numerade Educator