Question

3. If a price-taking firm's production function is given by q = 3vk, then its profit function is given by (b) 亚如

Answer 1

Profit = Total Revenue - Total cost

As it is price taking firm so price gets decided by market and lets assume the price as p

Total revenue = pq

hiring per unit of k is = v

Given, q = 3k^0.5 = k = q²/9

Therefore, TC = vk = vq²/9

So, Profit = TR - TC = pq - vq²/9

Lets take Profit as X

1^st order condition:

d(X)/dq = 0

=> p - 2vq/9 = 0

=> q = 9p/(2v)

Therefore, putting value of q,

X = pq - vq²/9

X = p(9p/(2v)) - v(9p/(2v))²/9

X = 9p²/(2v) - 9p²/(4v)

Profit = 9p²/(4v)

Correct option is (B) 9p²/(4v)