Chapter 5

Common fallacies Why are these statements wrong? (a) Since consumers do not know about indifference curves or budget lines, they cannot choose the point on the budget line tangent to the highest possible indifference curve. (b) Inflation must reduce demand since prices are higher and goods are more expensive.

Suppose films are normal goods but transport is an inferior good. How do the quantities demanded for the two goods change when income increases?

The own-price elasticity of demand for food is negative. The demand for food is inelastic. A higher food price increases spending on food. Higher food prices imply less is spent on all other goods. The quantity demanded of each of these other goods falls. Discuss each statement. Are they all correct?

Suppose Glaswegians have a given income and like weekend trips to the Highlands, which are a three-hour drive away. (a) If the price of petrol doubles, what is the effect on the demand for trips to the Highlands? Discuss both income and substitution effects. (b) What happens to the demand for Highland hotel rooms?

Frank's utility function for two goods, \(X\) and \(Y\), is given by \(U=X Y\). Find Frank's indifference curves, when utility is 10,20 and 30 . Plot these indifference curves. How should Frank compare the following two bundles: \((X=1, Y=10)\) and \((X=\) \(5, Y=2) ?\)

Suppose Frank has an income of \(£ 50\), the unit price of \(X\) is \(P_{X}=£ 2\) and the unit price of \(Y\) is \(P_{Y}=£ 1\). Write down the budget constraint for Frank. Knowing that the marginal rate of substitution (in absolute value) between \(X\) and \(Y\) is \(M R S=\) \(X / Y\), find the optimal bundle that Frank should consume. (Hint: at the optimal bundle, the absolute value of the \(M R S\) must be equal to the absolute value of the slope of the budget constraint. Moreover, the budget constraint must be satisfied. You need to solve a system of two equations in two variables, \(X\) and \(Y\).)

You can invest in a safe asset, in a risky asset, or in both. The safe asset has a guaranteed return of 3 per cent a year. The risky asset has an expected return of 4 per cent but it could be as much as 8 per cent or as little as 0 per cent. You decide to have some of your wealth in each asset. Now the expected return on the risky asset rises to 5 per cent; it could be as high as 9 per cent or as low as 1 per cent. Given the increase in the expected return on the risky asset, do you invest more of your wealth in the risky asset?

Suppose that Carl cannot tell the differences between a pack of British and a pack of Danish bacon. In a graph with British bacon on the vertical axis, plot some of Carl's indifference curves for British and Danish bacon, Suppose that Carl has an income of \(£ 20\). The price of Danish bacon is \(£ 2\) per pack, while the price of British bacon is \(£ 4\) per pack. Using the same graph, draw Carl's budget constraint and show his optimal bundle choice.

Essay question Consumer choice theory assumes that consumers are rational but we observe a person behaving differently in apparently similar situations. Is it realistic to think that we account for rational behaviour in every situation?

A consumer's income is \(£ 50\). Food costs \(£ 5\) per unit and films cost \(£ 2\) per unit. (a) Draw the budget line. Pick a point \(e\) as the chosen initial consumption bundle. (b) The price of food falls to \(£ 2.50\). Draw the new budget line. If both the goods are normal, what happens to consumption? (c) The price of films also falls to \(£ 1\). Draw the new budget line and show the chosen point \(e^{\prime \prime}\). (d) How does \(e^{\prime \prime}\) differ from \(e\) ? Why?