HW%202%20-%20key

# HW%202%20-%20key - 1 a Total Product 250 200 150 100 50 0 0...

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1 a. 1 - b & c) Equation for APL = Q/H = 100*H -2/3 MPL is less than APL for all values of H. 2 a) MPL = 3K 1/2 L -1/4 , so as L increases for some fixed value of K, the denominator is getting larger, so the total expression is getting smaller. Similar proof for MPK. 2 b) 0 50 100 150 200 250 0 2 4 6 8 10 12 14 Total Product Total Product 0 20 40 60 80 100 120 0 2 4 6 8 10 12 14 APL MPL

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MRTS = - MPL / MPK = -(3/2) * (K/L) 2 c) Let q =f(K,L) = 4K 1/2 L 3/4 The definition of IRS is that f(z*K,z*L)>z*f(K,L) for some z >1. Let, K =z*K and L =z*L. Therefore, q = f(z*K,z*L) = 4K 1/2 L 3/4 . Rewriting q leaves us with: q = 4K 1/2 L 3/4 = 4(z*K) 1/2 (z*L) 3/4 = z 1.25 4K 1/2 L 3/4 = z 1.25 q. Therefore, q = z 1.25 q. But since z>1 that means that z 1.25 > z. But this means q = z 1.25 q > z*q. This is just saying that f(z*K,z*L)>z*f(K,L), which is the definition for IRS. 3) False. MRTS = -MPL / MPK. If MPL is constant, then MPK must also be constant otherwise the MRTS will also change. Similarly, if MPK is constant, then MPL must also be constant otherwise the MRTS will also change. Perfect substitutes require that MRTS will always be constant, no matter what choice of inputs is used. Therefore, if only one of the marginal products is constant, it is not necessary that there are
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HW%202%20-%20key - 1 a Total Product 250 200 150 100 50 0 0...

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