Assume that a firm is producing a single product, that is differentiated from that of its...

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Assume that a firm is producing a single product, that is differentiated from that of its rivals. Assume further, that it has determined that its Average Revenue (AR) function, based on the demand function it faces (or estimates that it faces), is as follows: AR = PQ/Q = P = 0.1 Q¹+114 Qº-1.5 Q¹ -0.003 Q² [bear in mind that Q-¹ = 1/g, Q° = 1 and Q¹ = Q] and that its Total Cost (TC) function, for the same period, is determined to be: TC= 0.025Q³ -0.3Q² + 7.2Q¹ + 200Qº Required: [ assuming we are considering a "short-run" scenario in all cases] 1. Determine the profit-maximizing price for this product, given these revenue and cost functions 2. Determine the profit-maximizing quantity associated with that profit-maximizing price 3. What would the effect of an increase in the fixed cost element (the co-efficient of Qº_ in the TC function) be on the profit-maximizing price [Remember that Q° = 1 and that we are considering the short-run] 4. What would the effect of an increase in the co-efficient of Q¹ in the TC function be on the profit-maximizing quantity of output? [Remember that Q¹ = Q, and in this context, we are assuming the co-efficient of both Q³ and Q² respectively, remains the same] 5. Would a decrease in the co-efficient of Q¹ (= Q) in the TC function have the opposite effect compared to that in (4), or no effect on the profit-maximizing quantity of output ? 6. What would be the effect of a decrease in the co-efficient of Q³_in the TC function be on the profit-maximizing quantity of output ? 7. What would be the effect of a decrease in the co-efficient of Q2_in the TC function be on the profit-maximizing quantity of output ? [Remember that an "increase" in a negative number involves a smaller absolute value of that negative number until the zero-point (on the number line) is reached_ 8. What would the effect of an increase in the co-efficient of Qº in the AR function (and Q¹ the TR function) be on the profit-maximizing quantity of output? [Remember that Qº=1, and in this context, we are assuming the co-efficient(s) of Q² (and of any terms with higher powers of Q) remains/ remain the same.] 9. What would the effect of an increase in the co-efficient of Q¹ in the AR function (and Q² in the TR function) be on the profit-maximizing Price? [remember that Q¹-Q, and in this context, we are assuming the co-efficient(s) of Q² (and of any terms with higher powers of Q) remains/remain the same. Remember also, the close relationship between the respective coefficients of the AR, TR and MR versions of the revenue functions, and that an "increase" in a negative number involves a smaller absolute value of that negative number until the zero-point on the number line) is reached_1 10. Why might it not be economically realistic to assume that there is anything but a zero co- efficient on the Qºterm in an AR function ? Assume that a firm is producing a single product, that is differentiated from that of its rivals. Assume further, that it has determined that its Average Revenue (AR) function, based on the demand function it faces (or estimates that it faces), is as follows: AR = PQ/Q = P = 0.1 Q¹+114 Qº-1.5 Q¹ -0.003 Q² [bear in mind that Q-¹ = 1/g, Q° = 1 and Q¹ = Q] and that its Total Cost (TC) function, for the same period, is determined to be: TC= 0.025Q³ -0.3Q² + 7.2Q¹ + 200Qº Required: [ assuming we are considering a "short-run" scenario in all cases] 1. Determine the profit-maximizing price for this product, given these revenue and cost functions 2. Determine the profit-maximizing quantity associated with that profit-maximizing price 3. What would the effect of an increase in the fixed cost element (the co-efficient of Qº_ in the TC function) be on the profit-maximizing price [Remember that Q° = 1 and that we are considering the short-run] 4. What would the effect of an increase in the co-efficient of Q¹ in the TC function be on the profit-maximizing quantity of output? [Remember that Q¹ = Q, and in this context, we are assuming the co-efficient of both Q³ and Q² respectively, remains the same] 5. Would a decrease in the co-efficient of Q¹ (= Q) in the TC function have the opposite effect compared to that in (4), or no effect on the profit-maximizing quantity of output ? 6. What would be the effect of a decrease in the co-efficient of Q³_in the TC function be on the profit-maximizing quantity of output ? 7. What would be the effect of a decrease in the co-efficient of Q2_in the TC function be on the profit-maximizing quantity of output ? [Remember that an "increase" in a negative number involves a smaller absolute value of that negative number until the zero-point (on the number line) is reached_ 8. What would the effect of an increase in the co-efficient of Qº in the AR function (and Q¹ the TR function) be on the profit-maximizing quantity of output? [Remember that Qº=1, and in this context, we are assuming the co-efficient(s) of Q² (and of any terms with higher powers of Q) remains/ remain the same.] 9. What would the effect of an increase in the co-efficient of Q¹ in the AR function (and Q² in the TR function) be on the profit-maximizing Price? [remember that Q¹-Q, and in this context, we are assuming the co-efficient(s) of Q² (and of any terms with higher powers of Q) remains/remain the same. Remember also, the close relationship between the respective coefficients of the AR, TR and MR versions of the revenue functions, and that an "increase" in a negative number involves a smaller absolute value of that negative number until the zero-point on the number line) is reached_1 10. Why might it not be economically realistic to assume that there is anything but a zero co- efficient on the Qºterm in an AR function ?

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To solve the given questions lets go through each one step by step 1 To determine the profitmaximizing price we need to find the quantity that maximizes profit Profit is maximized when marginal revenu... View the full answer