A firm that produces its output in Asia and sells it in the United States has one plant in country 1 and another in country 2. Both plants have production function F(L,K) = LK. In country 1 the wage rate is W=1 and the price of capital R=1. In country 2 the rage rate is W=1 but the price of capital is R=4. In addition, in country 1 any plant that operates must pay a permit fee of $20,000 per month, while in country 2 any plant that operates must pay a permit fee of $10,000 per month. The permit fee is an avoidable fixed cost: if the plant is shut down it doesn't need to be paid. Assume for simplicity in what follows that there are no costs of shipping the product from Asia to the United States.
a) What is the cost function, marginal cost function, and average cost function for each plant?
b) What is the efficient scale and minimum average cost for each plant?
c) What is the cost function for the firm?