Question

Yusus unce you submit your answer. The e available from 4pm (PST) to 11:59pm (PST) today. Good luck! 1 pts Question 1 Consider a producer with technology given by 9 = min (K, $12) Consider a change in input prices, (w, t). If the firm produces the same quantity! before and after the change in input prices, what is the elasticity of substitution for this firm when it is minimizing long-run costs? O OOO O 9 Gen Intel Core 1-9750H PENER 6 Cores thet 2980 with Max-Q Design 2GB GDDR6 VRAM

Answer 1

When the inputs are needed in fixed proportions, (Q = min (K, 1/2L^2)) in that case the elasticity of substitution is 0 as the MRTS or the marginal rate of technical substitution of labour and capital along the isoquant of a fixed combination function of production changes from infinity to 0 as we go through the corners of the isoquant lines.

This kind of production function is called a fixed proportion production function. When a firm has this kind of a function, it cannot substitute between the inputs of labour and capital. We see that for this production, the firm needs 1/2*L^2 units of labour and 1 unit of capital to produce a good. This remains constant at all times. Increasing the labour or capital due to change in input prices of w and r is not going to be of any help as the minimum gets counted to identify the total production.

Let us consider that the firm has to produce 5 units of a good.

Q = 8. Thus K = 8 and / or 1/2*L^2 = 8 or L = sqrt (16) = 4

Now let us consider that the price of labour goes down to half so that double the labourers can be employed. Thus insyead of 4, we now can hire 8 labourers.

So 1/2*L^2 = 1/2 * 64 = 32

K is constant at 8.

So Q = 8.

Thus we see that it is not possible to change the production by having more of one resource unless the other also changes. So The marginal rate of technical substitution is 0.

Hence the elasticity of substitution for the firm in the long run to minimize costs is 0.

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