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?
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.
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?
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 \(-2\).
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?
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?
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?
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?
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?
