Question

The production of Florida strawberries uses two inputs: labor (L) and capital (K). The following production function describes how these inputs are combined to produce bushels of oranges. f(L,K) = 5(1/2 + 3K1/2 1) Determine what kind of returns to scale this production function exhibits (HINT: labor is the "x" variable - the one that goes on the horizontal axis). 2) What is the formula for that kind of returns to scale? (HINT: use f(L,K)) 3) What is the general formula for the technical rate of substitution? 4) What is the general formula for profit? 5) Suppose the price of a bushel of strawberries is $14, the wage is $7, and the rental rate is $3. In the short-run, capital is fixed at 16 units. Find the short-run profit-maximizing input, output, and the associated profit. 6) In the long-run, price, wage, and rental rate are the same as in the short-run. Find the long-run profit-maximizing inputs, output, and the associated profit. HTML Editora BIVA. AIX E 31 1 x

Answer 1

As per the HOMEWORKLIB POLICY, answering the first four parts

) f(2,6)= 52" + 3k"2 Augment production function by factor a. fal, ak)= 5(24)'n + 3(ka) = 5212442 + 392K"> = 212 [52'2 + 3 k"2] = 20.5 F (L,K) So, if we double the inputs Lk , then output is not increased by the doubled amount. F(lik) exhibits Decousing Returns to Scale 2) formula foo Diminishing Returns - A pooduction function Fll, k) has diminishing returns to scale if +221 F(al, ak) < af (2,K) * (lik) : . 3) General formula for MRTS - MRT SL,K - men MRTS – finns MPK 4) General formula for Profit - Poofit - TR - TC or Profit = px f(L,K) - TC