Question

6 (4 points) Suppose a non-price taking company owns a plant with some constant returns to scale production technology that produces robotic lawnmowers for two separable markets, the United States (U) and North Korea (N), each of which had some downward sloping demand function (us &respectively). In the short run what rule(s) should the companies follow to determine the profit maximizing quantity to produce for each market.

I understand that the question here has the answer. However, what I need help with is understanding the concepts/how they got the answer.

1. Is there any significance regarding the firm being a non-price taking firm? If so what is it?

2. What is "constant returns to scale"?
3. Is there any significance of the plants having constant returns to scale technology? If so what is it?

4. Is there any significance of the demand functions being downward sloping? If so what is it?

5. How does the info provided to us tell us what rule(s) the company should follow to determine the profit-maximizing quantity to produce for each market?

Answer 1

1. A non price taking firm is one which does not equate industry demand with industry supply to obtain the price at which it sells its goods. Instead, a non price taking firm is one which uses the industry demand function and determines its profit maximization quantity and price. One example of a non price taking firm is a monopoly. Let's understand this better with an example. Assume that the industry demand function is Q = 10 - P and Marginal Cost of production is 1.

Case 1: The firm is in a competitive market - The profit function of the firm is given by:

$\small \pi = PQ-Q$, maximizing the profit wth respect to Q gives P = 1. At P = 1, Q = 9. Profit of the firm = 9 - 1 = 8

Case 2: The firm is a non price taker (price setter) - The profit function of this firm is given by:

$\small \pi = (10-Q)Q-Q$, maximizing the profit with respect to Q gives Q = 4.5 At Q = 4.5, P = 5.5. Profit of the firm = 20.25

2. A production function shows constant returns to scale if an increase in all the variable inputs by X leads to an increase in total production by X. For example, comnsider the following production function:

F(L, K) = L + K
, increasing both L and K by X gives the following: $\small F(XL,XK)=XL+XK=X(L+K)=KF(L,K)$ which shows that this production function shows constant returns to scale.

3. Any monopolist firm's profit maximization quantity has to satisfy the condition that its Marginal Revenue must be equal to its Marginal Cost. Use the Case 2 example in the first part to check that we did just that to arrive at the profit maximization quantity of Q = 4.5 In that example, Marginal Cost = 1, Marginal Revenue = 10 - 2Q Equating these gave us Q = 4.5 The information that the firm uses a technology which shows constant returns to scale has no significance here, as the condition of MR = MC is always satisfied.

4. Demand functions are always downward sloping, following from the Law of Demand which states that with an increase in price, the quantity demanded of a good decreases. So, this information tells us that the firm cannot set price = infinity as the demand at that price would be zero.

5. Already described above.