What is the marginal rate of technical substitution for the production function y = (1200z₁z₂)^1/2 when Z₂=200 and z₁=100? A)200 B)2 C)100 D)1

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The expression for the marginal rate of technical substitution (MRTS) is given by MRTS = - (dU1/dU2)/(dS1/dS2). Given the production function, we have U1 = (1200zS1U1B11S1U1B0zS1U1B12S1U1B0)^(1/2) and U2 = S1U1P11/2S1S1P0. To find the MRTS, we need to take partial derivatives with respect to S1 and S2. Using the chain rule, we have:

dU1/dS1 = (1/2)*(1200zS1U1B11S1U1B0zS1U1B12S1U1B0)^(-1/2)*(1200zU1B11S1U1B0zS1U1B12S1U1B0 + 1200zS1U1B11S1U1B0zU1B12S1U1B0)

dU1/dS2 = (1/2)*(1200zS1U1B11S1U1B0zS1U1B12S1U1B0)^(-1/2)*(1200zU1B11S1U1B0zS1U1B12S1U1B0)

dU2/dS1 = (1/2)*S1U1P(-1/2)P11/2S1S1P0

dU2/dS2 = 0

Next, we need to evaluate these derivatives at the given values of zS1U1B12S1U1B0 and zS1U1B11S1U1B0. Plugging in the values, we get:

dU1/dS1 = 600

dU1/dS2 = 300

dU2/dS1 = (1/2)*(200^(-1/2))*100^(1/2) = 1

dU2/dS2 = 0

Therefore, the MRTS is:

MRTS = - (dU1/dU2)/(dS1/dS2) = - (dU1/dS2)/(dU2/dS2) = - (300/0) = undefined

This means that there is no well-defined MRTS for this production function at the given values of zS1U1B12S1U1B0 and zS1U1B11S1U1B0. Alternatively, we can say that the MRTS approaches infinity as S2 approaches zero. In general, for this production function, the MRTS depends on the values of zS1U1B11S1U1B0, zS1U1B12S1U1B0, and the levels of S1 and P1.

What Is the Marginal Rate of Technical Substitution for the Production