Question

3. Suppose a firm's technology was such that their isoquants for 100 units of output and 125 units of output looked like the ones depicted below. X2 20 18 16 14 12 10 9 125 4 9 100 2 4 6 8 10 12 14 16 18 20 XI If the price of input 1 and the price of input 2 are both $10/unit, can we tell how much input 1 will be used to produce 100 units of output in the cost minimizing way? If so, how much of input 1 should be used? If not, state why not. a. b. Consider two situations: (i) the prices of both inputs are $10/unit and the firm produces 100 units of output (same as above), (ii) the price of input 1 is twice the price of input 2 and the firm produces 125 units of output. Under which situation will the firm's demand for input 1 be greater if the firm is a cost minimizer?

Answer 1

Answer:

(a) Given, the price of input 1 is $10 per unit and the price of input 2 is $10 per unit.

At point E in the following diagram, the firm minimizes cost producing 100 units of output using 6 units of input 1 and 4 units of input 2 with a minimum cost of 6*$10+4*$10=$100. All other combinations of producing 100 output costs more that $100.

04 9-125 q- 100 2 4 6 8 10 12 14 16 18 20 X

(b)

Situation (i)

Given, the price of input 1 is $10 per unit and the price of input 2 is $10 per unit.

As discussed above the point E is the optimal combination of both the inputs where the firm minimizes cost producing 100 units of output using 6 units of input 1 and 4 units of input 2 with a minimum cost of $100.

Situation (ii)

Given, the price of input 1 is $20 per unit if the price of input 2 is $10 per unit.

With this price rate, the possible combination of inputs are A (4, 12), B (6, 10) and C (10, 8).

All these alternatives cost 200 (4*20+12*10), 220 (6*20+10*10) and 280 (10*20+8*10) respectively.

Thus point A is the cost minimizing combination of producing 125 units of output using 4 units of input 1 and 12 units of input 2. But between these two situations, the point E shows greater demand for input 1 than point A.