1.This question concerns information from the Labour Force Survey.

(a) Has the Canadian employment ratio recovered from the 1990-1992 recession?

(b) Find an identity linking the employment ratio, participation rate, and unemployment rate.

2.Imagine a labour market with two types of workers. Skilled workers make up 70 percent of the labour force. In each year, 5 percent of them experience a spell of unemployment, which lasts 2 months. Unskilled workers make up 30 percent of the labour force. Each year they have a 50 percent chance of experiencing a spell which lasts 3 months, and a 25 percent chance of experiencing a spell which lasts 12 months.

(a) What is the average length of an unemployment spell?

(b) What is the unemployment rate in a typical month?

3.This question explores how wealth, future income, and the interest rate affect consumption and saving. (Hint: Reading parts of Chapter 8 may help you answer this.) Suppose Shouyong's assets are denoted a, his income is denoted y, and his expected future income is denoted y ^f. His current consumption is c and his future consumption is c ^f. The present value of his consumption is limited by the present value of his resources:

c + c ^f/ (1+r) = a + y + y ^f/(1+r).

Furthermore, he tries to smooth his consumption over time, so that c = c ^f.

(a) If a=0, r=0.05, y=40 and y ^f=40 then what is his current consumption and saving?

(b) What is his consumption and savings if instead y ^f =60?

(c) Now suppose that, at this higher level of expected future income, the interest rate rises to r=0.08. What is his consumption and savings? Do changes in the interest rate have a large effect on his saving?

(d) Shouyong's parents bequeath him a gift of a=10. At y ^f=60 and r=0.08 what is the effect on his consumption and saving? Are the effects consistent with the predictions in the textbook?

4. Now suppose once again that a=0, r=0.05, y=40 and y ^f=40. Now add the realistic feature that Shouyong must pay taxes. Suppose that taxes are lump-sum in each period. Now the consumption plan must satisfy:

c + c ^f/ (1+r) = a + (y - t) + (y ^f - t ^f)/(1+r).

(a) Find consumption and savings if t=t ^f=10.

(b) Suppose that the government raises the current tax to a value of t=12, without changing its current or planned spending. What do you predict will be the effect on consumption and savings? (Hint: See pp 602-605)

5. A large chain of office equipment stores does a study of the relationship between inventory and subsequent sales at its various outlets. It finds the following relationship:

inventory	sales
100	40.0
101	40.5
102	40.7
103	40.8

(a) What is the marginal product of this form of capital?

(b) The firm finances inventory with a bank loan at a real interest rate of 8%. Inventory has a maintenance cost of 3%. How much inventory should each outlet carry?

(c) If its current inventory is 100 then what is its desired gross and net investment?

6.An economic historian studying Great Britain in the eighteenth century estimates the following relationships: Y ^fe=100; C ^d = 10 + 0.8Y - 100r; I ^d = 30 - 300r. In this question we shall treat this country as a closed economy.

(a) Draw the desired saving and investment curves.

(b) If G=10 solve for r, I, and C.

(c) Suppose that when Great Britain fought the seven years' war its public expenditure doubled to G=20. What are the predicted effects on the real interest rate, consumption, and investment?

1. (a) No. You can plot it (D773319) and see that during 1989 it exceeded 62. It fell through the recession and has not exceeded 59 since.
(b) er = (1-u)pr

2. To simplify, imagine there are 100 people in the labour force. Among skilled workers, 3.5 persons have a spell of 2 months each. There are 7 months of unemployment. Among unskilled workers, 15 persons have a 3 month spell and 7.5 persons have a 12 month spell.
(a) There are 26 spells, and 142 months of unemployment, so the average spell is 5.46 months.
(b) In any given month there are 7.5 unskilled workers on 12-month spells, 3.75 unskilled workers on a 3-month spell, and 0.583 skilled workers on a 2-month spell. The unemployment rate is 11.83.

3.(a) Clearly c=40 and s=y - c=0
(b) c=49.76, so s= y - c = -9.76
(c) c=49.615, so s= -9.615.
The change in the interest rate increases his saving (the income and substitution effects work in the same direction for borrowers) but the effect is small.
(d) Now c=54.80 and so s=-14.80. An increase in wealth increases consumption and reduces saving, as discussed in chapter 4.

4.(a) Clearly c=30 and s=y - t- c = 0.
(b) If Shouyong understands the government's budget constraint (as Ricardian equivalence) then he will not change his consumption. He will borrow 2 to pay his taxes, and repay it with interest from next period's tax cut of 2.1. But this assumes that (i) he can borrow at the same interest rate as the government and (ii) that he is not myopic and (iii) that the tax cut will occur while he is still alive. If these conditions do not hold then he may reduce his current consumption when taxes increase with no change in government spending.

5.(a) 0.5, 0.2, 0.1
(b) The user cost is 0.11, so the inventory level should be 102.
(c) The desired net investment is 2 so the gross investment is 5.

6.(a)I^d = 30-0.3r
S^d = 10+0.1r-G
(b) r=0.075, C=82.5, I=7.5
(c) r=0.10, C=80, I=0.