The demand for a monopolist's product is Q=700-5P. The monopolist also recognized that its...
Question:
The demand for a monopolist's product is {eq}Q=700-5P {/eq}. The monopolist also recognized that its marginal revenue is {eq}MR=140-0.2Q {/eq} and the marginal cost is $40. The firm is very happy there are no fixed costs.
i. What is the optimal price and quantity? What is the monopolist's revenue?
ii. Now the firm wants to engage in a price discrimination scheme. It sells 150 units for $100 and 150 units for $60. What is the profit in this scenario? Which strategy is more profitable?
Price Discrimination
Price Discrimination is the strategy generally followed by monopolists who want to maximize profits by charging different prices. Monopolists can charge either the highest price consumers willing to pay or price differentiating based on quantity or according to different consumers.
Answer and Explanation: 1
i.
{eq}\begin{align*} MR &= MC\\ 140 - 0.2Q &= 40\\ 100 &= 0.2Q\\ Q &= 500\\ Q &= 700 - 5P\\ 500 &= 700 - 5P\\ P &= \$ 40\\ TR &= 40 \times 500 = \$ 20000 \end{align*}{/eq}
ii.
Profitability of 2 schemes, PF1 and PF2:
{eq}\begin{align*} PF1 &= TR - TC\\ &= \left( {150 \times 100} \right) - \left( {40 \times 150} \right)\\ &= \$ 9000\\ PF2 &= TR - TC\\ &= \left( {150 \times 60} \right) - \left( {40 \times 150} \right)\\ &= \$ 3000 \end{align*}{/eq}
First straategy of charging $100 for 150 units is more profitable.
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