Part 1Suppose a production function for a firm takes the following algebraic form: Qequals= 33KLminus−(0.20.2)L2, where Q is the output of sweaters per day. Now suppose the firm is operating with 1010 units of capital (Kequals=1010) and 99 units of labour (Lequals=99). What is the output of sweaters? Part 1
A. 254254 sweaters per day B. 217217 sweaters per day C. 268268 sweaters per day D. 209209 sweaters per day E. 7474 sweaters per day

Question

Part 1Suppose a production function for a firm takes the following algebraic​ form: Qequals= 33KLminus−​(0.20.2​)L2​, where Q is the output of sweaters per day. Now suppose the firm is operating with 1010 units of capital ​(Kequals=1010​) and 99 units of labour ​(Lequals=99​). What is the output of​ sweaters? Part 1
A. 254254 sweaters per day B. 217217 sweaters per day C. 268268 sweaters per day D. 209209 sweaters per day E. 7474 sweaters per day

BlackTom AI · Accepted Answer

We start by restating the problem to ensure clarity: we have a production function Q = 33KL − (0.20.2) L^2, with K = 10 and L = 9, and we must determine Q and compare to the given answer choices.

Option A: 254 sweaters per day. To assess this, plug K = 10 and L = 9 into the function. If we interpret (0.20.2) as the product 0.2 × 0.2 = 0.04, then Q = 33 × 10 × 9 − 0.04 × 9^2 = 2970 − 3.24 = 2966.76. This is far from 254, so option A is incorrect.

Option B: 217 sweaters per day. Using the same calculation as above (Q ≈ 2966.76), 217 is not equal to the computed value, so option B is also incorrect.

Option C: 268 sweaters per day. Again, the computed Q ≈ 2966.76 does not match 268, making option C incorrect.

Option D: 209 sweaters per day. Since the calculated output is roughly 2966.76, 209 does not align with the result, so option D is incorrect.

Option E: 74 sweaters per day. This is also not equal to the computed Q of about 2966.76, so option E is incorrect.

Overall, when we substitute K = 10 and L = 9 into the given function with the interpretation that (0.20.2) equals 0.04, the output Q is 2966.76, which does not correspond to any of the listed options A–E. If we cross-check with the provided answer note stating Q = 1009.8, there is a discrepancy either in the interpretation of the function or in the stated numerical result. The essential point is that none of the listed choices matches the calculated output under the standard interpretation of the expression, so no option is correct in that sense.

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