SM 3. Consider the problem of Example 12.4.2. (a) Suppose that Q=f(L) = √L. Write down Eq. (*) in this case and find an explicit expression for L* as a function of P and w. Find the partial derivatives of L* w.r.t. P and w. Then verify the signs obtained in the example. (b) Suppose the profit function is replaced by л(L) = Pf (L) – C(L, w), where C(L, w) is the "cost function". What is the first-order condition for L* to be optimal in this case? Find the partial derivatives of L* w.r.t. P and w. EXAMPLE 12.4.2 A firm produces Q=f(L) units of a commodity using L units of labour. We assumethat f'(L)> 0 and f" (L) <0, sof is strictly increasing and strictly concave.³ SM 3. Consider the problem of Example 12.4.2.(a) Suppose that Q=f(L) = √L. Write down Eq. (*) in this case and find an explicit expressionfor L as a function of P and w. Find the partial derivatives of L* w.r.t. P and w. Then verifythe signs obtained in the example.(b) Suppose the profit function is replaced by (L) = Pf (L) -C(L, w), where C(L, w) is the"cost function". What is the first-order condition for L* to be optimal in this case? Find thepartial derivatives of L* w.r.t. P and w..

The first order condition is written as

Answered: . Consider the problem of Example…

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Chapter1: Making Economics Decisions

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SM 3. Consider the problem of Example 12.4.2. (a) Suppose that Q=f(L) = √L. Write down Eq. (*) in this case and find an explicit expression for L* as a function of P and w. Find the partial derivatives of L* w.r.t. P and w. Then verify the signs obtained in the example. (b) Suppose the profit function is replaced by л(L) = Pf (L) – C(L, w), where C(L, w) is the "cost function". What is the first-order condition for L* to be optimal in this case? Find the partial derivatives of L* w.r.t. P and w.

EXAMPLE 12.4.2 A firm produces Q=f(L) units of a commodity using L units of labour. We assume
that f'(L)> 0 and f" (L) <0, sof is strictly increasing and strictly concave.³

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