Consider a firm with market power who wants to use a two-part pricing strategy (T,P). There are N1 = 200 customers with demand P = 10 – Q1 and N2 = 300with demand P = 15 – Q2 . The firm has zero fixed costs and constant marginal cost C = $4. –Hint: Recall that if P = a1 – Q1 and P = a2 – Q2 , with a2 > a1 , then the derivative of ( N1 + N2 )*T(P) + (P-c)*[ N1 *( a1 – P) + N2 *( a2 – P)] with respect to P, where T(P) = (a1 – P)2 / 2, is given by -( N1 + N2 )*( a1 – P) + N1 * ( a1 – P) + N2 *( a2 – P) – (P-c)*( N1 + N2 ). If the firm wants to sell to only one of the two groups, then It will set T = $18 and obtain profits equal to $3,600 It will set T = $18 and P = $10 It will set T = $60.5 and obtain profits equal to $18,150 None of the above
Consider a firm with market power who wants to use a two-part pricing strategy (T,P). There
are N<sub>1</sub> = 200 customers with demand P = 10 – Q<sub>1</sub> and N<sub>2</sub> = 300with demand P = 15 – Q<sub>2</sub> . The firm has zero fixed costs and constant marginal cost C = $4. –Hint: Recall that if P = a<sub>1</sub> – Q<sub>1</sub> and P = a<sub>2</sub> – Q<sub>2</sub> , with a<sub>2</sub> > a<sub>1</sub> , then the derivative of ( N<sub>1</sub> + N<sub>2</sub> )*T(P) + (P-c)*[ N<sub>1</sub> *( a<sub>1</sub> – P) + N<sub>2</sub> *( a<sub>2</sub> – P)] with respect to P, where T(P) = (a<sub>1</sub> – P)<sup>2 </sup>/ 2, is given by -( N<sub>1</sub> + N<sub>2</sub> )*( a<sub>1</sub> – P) + N<sub>1</sub> * ( a<sub>1</sub> – P) + N<sub>2</sub> *( a<sub>2</sub> – P) – (P-c)*( N<sub>1</sub> + N<sub>2</sub> ). If the firm wants to sell to only one of the two groups, then <table><tbody><tr><td> It will set T = $18 and obtain profits equal to $3,600 </td> </tr><tr><td> It will set T = $18 and P = $10 </td> </tr><tr><td> It will set T = $60.5 and obtain profits equal to $18,150 </td> </tr><tr><td> None of the above</td> </tr></tbody></table>
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