Worked Problems

Suppose a firm's short-run total product schedule is given in the table below. It sells its output competitively for $1.50 each.

Labour	Total Product	Marginal Product	Marginal Revenue Product
0	0
1	8
2	18
3	29
4	39
5	47
6	52
7	53
8	53

What is the marginal product of the 1st worker?
What is the marginal revenue product of the first worker?
Suppose the wage is $7. How many workers will this firm hire?
If the wage rises to $9, how will the firm adjust its employment?
Alternatively, suppose the firm sells its output according to the following demand schedule:
Labour Total Product Product Price Marginal Product Marginal Revenue Product
0 0 ----
1 8 $ 3.50
2 18 2.80
3 29 2.30
4 39 1.90
5 47 1.65
6 52 1.50
7 53 1.40

Fill in the remaining two columns of the table. How many workers will be hired at a wage of $7?

Suppose a firm's marginal product of capital and marginal product of labour schedules are as shown in the table below. The firm hires both capital and labour competitively for $4 and $8, respectively. Its output is sold competitively for $.50 each.

Capital	MP of Capital	Labour	MP of Labour
0		0
1	10	1	28
2	9	2	30
3	8	3	24
4	7	4	20
5	6	5	16
6	5	6	12
7	4	7	8
8	3	9	4

Suppose the firm is currently using 4 units of capital and 4 units of labour. Is the corresponding output being produced at least cost? How do you know?
What is the profit-maximizing combination of labour and capital the firm should use?
What output level corresponds to the input combination you just found? Is this the least-costly combination of labour and capital to produce this level of output?

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