Question $1$: Paul loves hot drinks, and he has a part of his weekly budget earmarked for

buying them. In the diagram below, you can find three examples IC$1,$ IC$2$ and IC$3$ for

indifference curves that represent Paul's preferences for tea and coffee, and three examples

$x,Y$ and $Z$ for specific bundles of weekly tea and coffee consumption.

a$)$ Compare bundles $Z$ and $Y$ by explaining

a$1)$ which of these bundles includes more tea, and

a$2)$ which of these bundles Paul likes better.

b$)$ Assume that $x$ is Paul's optimal bundle. Draw Paul's budget line under this

assumption.

f$)$ Place a dot in the above diagram for the following bundles of weakly tea and coffee

consumption if such a bundle exists and label each dot according to the bundle it

represents. If no bundle with the required properties exists, explain why it can't exist.

c$5)$ Bundle A: A uses up exactly all of Paul's budget for hot drinks but includes less

coffee than $x.$

c$6)$ Bundle B: Paul prefers $x$ over $B$ and $B$ over $Z.$

c$7)$ Bundle C: Paul prefers Y over C but can't afford bundle C$,$ although C includes

less tea than $Y.$

c$8)$ Bundle D: Paul prefers any of the bundles X$,$ Y and Z over D$,$ although D includes

more tea than these other three bundles $x,Y$ and $Z.$ He can't afford bundle D$.$

g$)$ The price of tea is $1\mathrm{.}50$ per cup, and that of coffee is $3$ per cup. Assuming that

Paul's weekly budget for hot drinks is $15,$ write the appropriate quantities at the

intercepts of Paul's budget line with each axis!

h$)$ During a cold weather spell, Paul increases his budget for hot drinks. As a consequence, some other bundle N will now be optimal for Paul. Paul tells you that bundle N includes more coffee than bundle Z in the diagram. Carefully argue which of the bundles N or Z Paul likes better.