Question

You have $1,000 that you can invest. If you buy General Motors stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.4 you will get $1,600; with a probability of 0.4 you will get $1,100; and with a probability of 0.2 you will get $800. If you put the money into the bank, in one year's time you will get $1,100 for certain.

What is the expected value of your earnings from investing in General Motors stock?

A $649 B $240 C$1000 D $1240

Suppose you prefer putting your money into the bank to investing it in General Motors stock. What does that tell us about your attitude to risk?

A You must be risk-averse: you are willing to take a lower (but certain) payoff instead of a higher (but risky) one.

B You must not be risk-averse: you are willing to take a lower (but certain) payoff instead of a higher (but risky) one.

C  It tells us nothing; you are willing to take a higher (but certain) payoff instead of a lower (but risky) one.

D You must be risk-averse: even though the two payoffs are the same, you prefer the one that is certain.

You are the governor's economic policy adviser. The governor wants to put in place policies that encourage employed people to work more hours at their jobs and that encourage unemployed people to find and take jobs. Assess the following policy in terms of reaching that goal. Choose the response that correctly explains your reasoning in terms of income and substitution effects, and indicates when the impact of the policy may be ambiguous.
The state income tax rate is lowered, which has the effect of increasing workers' after-tax wage rate.

A The effect of this policy on the incentive to work is ambiguous.

B This policy will unambiguously encourage people to work less.

C This policy will unambiguously encourage people to work more.

Answer 1

The returns from General Motor's along with the respective probabilities can be summed up as follows:

Returns (x) ($)	Probability (P(x))	xP(x) ($)
1600	0.4	640
1100	0.4	440
800	0.2	160

Therefore the Expected value of earnings from investing in General Motor’s is:

640 + 440 + 160 = Option D : $1240.

As opposed to General Motor’s since there is certainty of earning $1,100 from the bank, the probability is 1 and the expected value of earning from bank = $1100.

Since the expected value of earnings from investing in General Motor’s is greater than the expected value of earning from bank, investing in General Motor’s is a wiser option.

If in spite of the higher expected value of earnings from investing in General Motor’s, the money is put into the bank then it means that the behaviour is risk averse. This is because, the decision to choose the sure or certain option with lower guaranteed return implies that there is a tendency to avoid risk, even with a higher possible return.

Therefore the first option is correct, which says that:

1. You must be risk-averse: you are willing to take a lower (but certain) payoff instead of a higher (but risky) one.

When a policy is chosen that lowers the state income tax-rate and raises workers’ after-tax wage rate, the following possibilities surface:

Firstly, it is common knowledge that higher tax rates discourage workers to work harder. This is because, despite working harder, a greater proportion of their wages are taxed and their in-hand pay reduces, which makes them want to work for less hours and enjoy more hours of labour instead. Therefore, a tax-cut generally increases the incentive for the employed person to work more and earn more. However, it also depends on what the preference of every worker is. If some worker wants to be just as better off and earn just as much as he was earning previously, then he might want to trade labour for more hours of leisure. This is illustrated through fig 1 and fig 2. In fig 1, the initial time allocation budget line is given by AB. When tax rate falls, the wage rate increases and the time allocation budget line ROTATES to A’B. This is because, when the worker works for 0 hours and enjoys maximum labour in both the cases, his earning amount to 0. Leisure is measured on the horizontal axis from left to right and labour, on the same horizontal axis from right o left, where Labour = 24- leisure (as there are 24 hours in a day).

The income effect (IE) is measured by the parallel shift of the initial time-allocation budget line and a shift from point E₁ to E₂ where E₁ is at the point of tangency of Indifference Curve 1 (IC₁) and AB. E₂ is at the point of tangency of IC₂ and A’’B’ (the parallel shift of the time-allocation budget line). This results in enjoying more hours of leisure. The substitution effect (SE) is at point E₃ which is at the point of tangency of A’B and IC_2. This results in working harder, for longer hours.

Fig 2 shows a backward bending supply curve where after a certain level of income, the employed person doesn’t want to work harder, even if there are tax cuts and wage raises. So the impact of a tax cut on the efficiency and incentive to work is ambiguous. It depends on which effect dominates the other. In cases where |SE|>|IE|, the employee works harder for longer hours. In cases where |IE|>|SE|, the employer works for less hours and enjoys more leisure even though there are tax cuts.

It is also important to note that people who are unemployed and are looking for jobs, will always tend to work for longer hours in order to earn more and save more. They do not generally choose leisure during tax cuts and takes full advantage of low taxes to earn higher income. But the overall impact of the policy depends on what stage of earning which person is in. Thus, the overall impact of the policy is ambiguous.

It is also worthwhile to discuss the trade-off that is generated with a fall in the tax rate. When the tax rate falls and employees do in fact work harder, their efficiency increases and the need for firms to hire unemployed workers looking for a job, reduces. Thus, it is less likely that unemployed people will find jobs when already employed people start working for longer hours and become more productive. Therefore with this trade-off, the impact of a tax-cut on unemployed people’s incentive to look for jobs becomes all the more ambiguous.

Thus, when “the state income tax rate is lowered, which has the effect of increasing workers' after-tax wage rate”, then option A holds true where ‘the effect of this policy on the incentive to work is ambiguous.’