500359 – MICROECONOMICS – 2019/20
Class Exercises
Problem Set 4
1
(i)
Write out the budget constraints for the following combination of prices and
income: P
X
= 5, P
Y
= 2, M = 10
(ii)
For the budget constraint in (i) above, calculate the slope and points where the line
crosses the X-axis (X
max
) and Y-axis (Y
max
).
Draw the budget constraint on a graph.
(iii)
Show what happens to the slope and position of the budget constraint in (i) when:
(a)
P
X
doubles;
(b)
P
Y
and P
X
both double;
(c)
P
Y
falls to 1.5;
(d)
M increases by 5.
2
Consider a consumer with preferences for apples (A) and bananas (B) given by the utility
function U = AB.
Let the prices of apples and bananas be £1 per unit and £2 per unit
respectively, and let the consumer’s total available budget for the two goods be £12.
(i)
On a graph (with apples (A) on the horizontal axis and bananas (B) on the vertical
axis) draw the indifference curves for U = 12, U = 18 and U = 24.
On the same
graph plot the budget constraint and identify (without the use of algebra) the
optimal choice (utility maximising) of apples and bananas.

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- Fall '19
- Economics, Utility