Question

The table below shows three different technologies used to produce various levels of output.

Output	Tech 1		Tech 2		Tech 3
	K	L	K	L	K	L
1	6	1	4	4	2	7
2	7	3	6	6	3	10
3	9	5	8	8	4	14
4	12	7	10	10	5	20
5	15	9	12	12	6	26
6	21	11	14	14	7	32

(a)        In general, which technology is the most desirable?

(b)       Which technology will be chosen if the firm wishes to produce 1 unit of output, the price of capital is $4 per unit, and the price of labor is $2 per unit?

(c)        Will this still be cheapest if the input prices change to $3 and $3, respectively?

(d)       Will this still be cheapest if the input prices change to $2 and $4, respectively?

(e)        For each of the three sets of prices in (b), (c), and (d) above, establish which technology is the cheapest for each output level.

Answer 1

Answer

(a) in general, the least cost technology is most desirable. If there are more than one technology that can produce the same level of output, then the technology for which the cost of production is the lowest, that technology is most desirable.

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(b) Technology 3

If the price of capital is $4 per unit, and the price of labor is $2 per unit, let us see the cost of production of producing 1 unit of output using technology 1, technology 2, and technology 3.

For producing 1 unit of output, technology 1 requires 6 units of capital(K) and 1 unit of labor(L).

Cost of production(C1) = $4 * 6 + $2 * 1

Or,  Cost of production(C1)= $24 + $2 = $26

For producing 1 unit of output, technology 2 requires 4 units of capital(K) and 4 units of labor(L).

Cost of production(C2) = $4 * 4 + $2 * 4

Or,  Cost of production(C2)= $16 + $8 = $24

For producing 1 unit of output, technology 3 requires 2 units of capital(K) and 7 units of labor(L).

Cost of production(C3) = $4 * 2 + $2 * 7

Or,  Cost of production(C3)= $8 + $14 = $22

From the above three total costs, we conclude that technology 3 will be chosen to produce 1 unit of output because technology 3 is the least cost technology.

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(c) Technology 1

If the price of capital is $3 per unit, and the price of labor is $3 per unit, let us see the cost of production of producing 1 unit of output using technology 1, technology 2, and technology 3.

For producing 1 unit of output, technology 1 requires 6 units of capital(K) and 1 unit of labor(L).

Cost of production(C1) = $3 * 6 + $3 * 1

Or,  Cost of production(C1)= $18 + $3 = $21

For producing 1 unit of output, technology 2 requires 4 units of capital(K) and 4 units of labor(L).

Cost of production(C2) = $3 * 4 + $3 * 4

Or,  Cost of production(C2)= $12 + $12 = $24

For producing 1 unit of output, technology 3 requires 2 units of capital(K) and 7 units of labor(L).

Cost of production(C3) = $3 * 2 + $3 * 7

Or,  Cost of production(C3)= $6 + $21 = $27

From the above three total costs, we conclude that when the prices of inputs change to $3 both, technology 1 will be chosen to produce 1 unit of output because technology 1 is the least cost technology with this input prices..

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(d) Technology 1

If the price of capital is $2 per unit, and the price of labor is $4 per unit, let us see the cost of production of producing 1 unit of output using technology 1, technology 2, and technology 3.

For producing 1 unit of output, technology 1 requires 6 units of capital(K) and 1 unit of labor(L).

Cost of production(C1) = $2 * 6 + $4 * 1

Or,  Cost of production(C1)= $12 + $4 = $16

For producing 1 unit of output, technology 2 requires 4 units of capital(K) and 4 units of labor(L).

Cost of production(C2) = $2 * 4 + $4 * 4

Or,  Cost of production(C2)= $8 + $16 = $24

For producing 1 unit of output, technology 3 requires 2 units of capital(K) and 7 units of labor(L).

Cost of production(C3) = $2 * 2 + $4 * 7

Or,  Cost of production(C3)= $4 + $28 = $32

From the above three total costs, we conclude that technology 1 will be chosen to produce 1 unit of output because technology 1 is the least cost technology with this input prices.

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(e)

Technology 1	Cost of production
Output	K	L	Price of K = $4 per unit, Price of L = $2 per unit
1	6	1	$24 + $2 = $26
2	7	3	$28 + $6 = $34
3	9	5	$36 + $10 = $46
4	12	7	$48 + $14 = $62
5	15	9	$60 + $18 = $78
6	21	11	$84 + $22 = $106

Technology 2	Cost of production
Output	K	L	Price of K = $3 per unit, Price of L = $3 per unit
1	4	4	$12 + $12 = $24
2	6	6	$18 + $18 = $36
3	8	8	$24 + $24 = $48
4	10	10	$30 + $30 = $60
5	12	12	$36 + $36 = $72
6	14	14	$42 + $42 = $84

Technology 3	Cost of production
Output	K	L	Price of K = $2 per unit, Price of L = $4 per unit
1	2	7	$4 + $28 = $32
2	3	10	$6 + $40 = $46
3	4	14	$8 + $56 = $64
4	5	20	$10 + $80 = $90
5	6	26	$12 + $104 = $116
6	7	32	$14 + $128 = $142

For output level 1 - Technology 2 is the cheapest

For output level 2 -  Technology 1 is the cheapest

For output level 3 - Technology 1 is the cheapest

For output level 4 - Technology 2 is the cheapest

For output level 5 - Technology 2 is the cheapest

For output level 6 - Technology 2 is the cheapest

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