Under perfect competition, there is a firm producing two products. Quantity of first product is q1 and quantity of second product is q2 . Prices of both commodities must be taken as exogenous. The price of first product is given by p1 = 5 and the price of second product is given by p2 = 3. The firm’s cost function is assumed to be C = 2q1 2 + 2q2 2 + q1q2. Find out the following:

a) firm’s revenue function

b) firm’s marginal cost function for first product

c) firm’s marginal cost function for second product

d) firm’s profit function

e) the value of q1 and q2 that maximise the firm’s profits

f) Value of Hessian matrix

a) The firm's revenue function is given by:

R = p1q1 + p2q2
= 5q1 + 3q2

b) The firm's marginal cost function for the first product (MC1) is given by:

MC1 = dC/dq1 = 4q1 + q2

c) The firm's marginal cost function for the second product (MC2) is given by:

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