Question

Suppose that firms in a monopolistically competitive industry each face an inverse demand given by curve in the foreign country market given by P = 60 − 4Q. Firms can choose to serve the foreign market either by exporting or by foreign direct investment (FDI).

a) Serving the foreign market by export requires the firm to incur a fixed cost of FX = 49, a marginal cost of c and a per unit trade cost of t = 8 per unit. Write out the expression for firm profit from exporting and solve for the profit maximizing quantity in the foreign market as a function of the firm’s marginal cost. Show that the profit of the firm is decreasing and convex in c, with a slope equal to −Q(c + t). What is the maximum level of c at which it will be profitable to serve the foreign market by export?
b) If the firm chooses to become multinational and serve the foreign market by producing in a foreign affiliate, it must incur a fixed cost of FF DI = 100 but avoaids the trade cost. The marginal cost of production in the foreign market is assumed to be c, the same as in the domestic market. Solve for profits from FDI as a function of c.
c) Using your answers to (b) and (c), explain which firms will choose exporting, which will choose FDI, and which will not sell to the foreign market.

Answer 1

To calculate the profit from exporting, we subtract the costs from the revenue, while the profit from FDI can be calculated in a similar way. The profit maximizing quantity in the foreign market as a function of the firm's marginal cost is given by (P - c - t) / 2. The profit is decreasing and convex in c, with a slope equal to -Q(c + t). The maximum level of c at which it will be profitable to serve the foreign market by export is when c = P - t. Firms will choose exporting, FDI, or not sell to the foreign market based on the comparison of profits.

Step-by-step explanation:

To calculate the profit from exporting, we need to subtract the costs from the revenue. The revenue can be calculated as the product of the price (P) and the quantity (Q). The cost includes the fixed cost (FX), the variable cost (c) multiplied by the quantity (Q), and the per unit trade cost (t) multiplied by the quantity (Q). The expression for firm profit from exporting is:

Profit = (P - c)Q - (FX + tQ)

To find the profit maximizing quantity in the foreign market, we can differentiate the profit expression with respect to Q, set it equal to zero, and solve for Q. The profit maximizing quantity is:

Q = (P - c - t) / 2

To show that the profit is decreasing and convex in c, we can differentiate the profit expression with respect to c twice. The first derivative represents the slope of the profit function, which is equal to -Q(c + t). The second derivative represents the curvature of the profit function, which is negative. Therefore, the profit is decreasing and convex in c. The maximum level of c at which it will be profitable to serve the foreign market by export is when the profit is zero, so:

c = P - t

For part (b) and (c), the profit from Foreign Direct Investment (FDI) can be calculated as:

Profit = (P - c)Q - FF_DI

Comparing the profit from exporting and FDI, a firm will choose exporting if the profit from exporting is greater than the profit from FDI, a firm will choose FDI if the profit from FDI is greater than the profit from exporting, and a firm will not sell to the foreign market if both profits are negative.