A multinational firm produces microchips at a home facility and at a foreign subsidiary according to the respective cost functions C H 120Q H and C F 50Q F 5Q F 2 The firm sells chips in the home market and the foreign market where the inverse demand curves are P H 300 D H and P F 250 5D F , Respec...

a Using the spreadsheet optimizer we determine the multinati ...

A multinational firm produces microchips at a home facility and at a foreign subsidiary according to the

Question:

A multinational firm produces microchips at a home facility and at a foreign subsidiary according to the respective cost functions:

C_H = 120Q_H and C_F = 50Q_F + .5Q_F²

The firm sells chips in the home market and the foreign market where the inverse demand curves are

P_H = 300 − D_H and P_F = 250 − .5D_F,

Respectively: Here D denotes the quantity sold in each market, and Q denotes the quantity produced in each facility. Chips can be costlessly shipped between markets so that DH need not equal QH (nor D_F equal Q_F). However, total production must match total sales: Q_H + Q_F = D_H + D_F.

a. Create a spreadsheet (based on the accompanying example) to model the firm’s worldwide operations. Use the spreadsheet optimizer to find the firm’s profit-maximizing outputs, sales quantities, and prices.

(Be sure to include the constraint that cell F9—extra output—must equal zero. That is, total sales must exactly equal total output.) Are chips shipped overseas? At the optimal solution, confirm that MR_H = MR_F = MC_H = MC_F.

A multinational firm produces microchips at a home facility and

b. Answer the questions in part a under an "antidumping" constraint; that is, the company must charge the same price in both markets. (Include the additional constraint that cell F12, the price gap, must equal zero.)