A firm is a monopolistic producer of two goods G_{l} and G_{2} The prices are related to quantities Q_{1} and Q_{2} according to the demand equations P_{1} = 50 - Q P_{2} = 90 - 2O_{2} If the total cost function is TC = Q_{1} ^ 2 + 2Q_{1}*Q_{2} + Q_{2} ^ 2 (a) Determine th
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BCPC 208: QUANTITATIVE METHODS
ASSIGNMENT 8
1. A firm is a monopolistic producer of two goods G_{l} and G_{2} The prices are related to quantities
Q_{1} and Q_{2} according to the demand equations
P_{1} = 50 - Q
P_{2} = 90 - 2O_{2}
If the total cost function is
TC = Q_{1} ^ 2 + 2Q_{1}*Q_{2} + Q_{2} ^ 2
(a) Determine the firm's profit function,
(b) Find the values of Q_{1} and Q_{2} which maximises profit by applying first and second order conditions.
(e) Find the maximum profit and deduce the prices that maximises profit
2. A monopolistic producer of two goods, G_{1} and G_{2} has a joint total cost function TC = 5Q_{1} + Q_{1}*Q_{2} + 5Q_{2}
where Q_{1} and Q_{2} denote the quantities of G_{1} and G_{2} respectively. If P_{1} and P_{2} denote the corresponding prices, then the demand equations are
Q_{1} = 40 - P_{1} + Q_{2}
Q_{2} = 20 + 2Q_{1} - P_{2}
(a) Find the total revenue function for each good.
(b) Find the profit function for the firm
(c) Find the maximum profit if the firm is contracted to produce a total of 12 goods of either
type.
(d) Find the price that the firm is supposed to charge for each good.
(e) Estimate the new optimal profit if the production quota increases by 2 unit.
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