Torti has Cobb-Douglas utility given by U = I x L, where I is income to spend on goods

and services and L is hours of leisure. He can allocate 24 hours between leisure and working at a

wage of $20 per hour. Assume that income is measured on the vertical axis and hours of leisure are

measured on the horizontal axis, such that Torti has indifference curves with a slope (ie, marginal

rate of substitution) of -(I / L). (Note: you will likely find that a diagram is extremely helpful to

visualise the concepts.)

a. (2 marks) Write down Torti's budget constraint in the form of an equation for a straight line (ie,

y = mx + b).

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b. (2 marks) Use part (a) and the information provided about his indifference curves to write down

the optimal relationship between I and L.

c. (2 marks) Use parts (a) and (b) to calculate Torti's utility-maximising level of income and

leisure.

Assume that the government introduces a universal basic income (UBI) of $200 per day.

d. (2 marks) Rewrite Torti's budget constraint in the form of an equation for a straight line (ie, y =

mx + b).

e. (2 marks) Use part (d) to calculate Torti's new utility-maximising level of income and leisure.

(Hint: the slopes of the indifference curves and the budget constraint are unchanged so the

optimal relationship between I and L is unchanged.)

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f. (2 marks) Briefly explain if and why the amount Torti spends on goods and services goes up by

more than the UBI, less than the UBI or exactly equal to the UBI.

Assume that the government replaces the UBI with a welfare programme that pays $200 per day for

anybody who does not work at all but claws it back at a rate of 50 percent for each dollar earned

until the $200 is paid back.

g. (2 marks) Rewrite Torti's budget constraint in the form of an equation for a straight line (ie, y =

mx + b). (Hint: there is a kink in his budget constraint where the welfare is fully clawed back.

You will need to describe both parts of the constraint.)

h. (2 marks) Use part (g) and the information provided about his indifference curves to write down

the optimal relationship between I and L. (Hint: assume that the optimal point occurs where he

receives some amount of welfare.)