12. Consider a firm that has the production function f(x) = λx + ³x³. a. What is required for this to be a price taking firm? b. In a short paragraph, explain the logic behind such requirement(s). c. Following your answer from the previous items, what condition(s) on the parameters must hold?
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- Explain why a firm might want to produce its good even after diminishing marginal returns have set in and marginal cost is on the rise. People often believe that large firms in an industry have cost advantages over small firms in the same industry. For example, they might think a big oil company has a cost advantage over a small oil company. For this to be true, what condition must exist? Explain your answer.What happens to a competitive firm whose cost function exhibits decreasing marginal cost everywhere? Construct a concrete cost function of this type and carry out the search for the profit-maximizing output.For each of the following events identify which of the determinates of demand or supply are affected. Also indicate whether demand or supply is increased or decreased. Why? A stock market crash lowers people’s wealth. Batelco increases the prices of mobile services. Diminishing returns mean rising costs while economies of scale mean falling costs. Therefore, a firm cannot be facing both diminishing returns and economies of scale. Do you agree? Why or why not?
- Suppose that the market for apples is perfectly competitive. Production of apples requires two inputs:workers (L) and land (K). The production function for apples is:F(K,L)=3K^(1/3)* L^(2/3) A) Suppose that W=4, R=16, and in the short-run, K=27. Find the firm’s short-run cost function SRC(q)and short-run marginal cost function SRMC(q).B) What is the optimal production of apples if P=4? What are consumer surplus and profit?C) Find the firm’s short-run supply of apples Q(P) when W=4, R=16 and K=27.D) Find the firm’s long-run cost function LRC(q) and long-run marginal cost function LRMC(q) when W=4and R=16. How do these compare to the firm’s short-run cost function and marginal cost function?E) Find the firm’s long-run supply of apples q(P) when W=4 and R=16.Suppose a perfectly competitive firm uses labor and capital to produce. In the short run, the quantity of labor is variable and the quantity of capital is fixed. The cost curve estimated by the manufacturer based on capital and labor is: *EQUATION ATTACH AS PHOTO, a. What is the lowest price the manufacturer expects in the long run?b. If factors prices remain constant, what is the lowest product price that firms will continue to operate in the short run?c. If the product price is $120 , how many products will the manufacturer produce in the short run?suppose the average variable cost of production is $15 when output equals 110 haircuts and $17.26 when output equals 140 haircuts. If the firm wants to maximize profit how many haircuts will it produce at what cost? explain your answer.
- What is the value of the average cost? If the price in the market of the perfect competitive firm is P9 Equilibrium quantity would be? Why?Consider the following production function: Q = (1-x-1)yk. Assume we are dealing with the short run, so capital is fixed, i.e. k=1. Assume the prices of both inputs x and y are 1 and the cost of capital is r = 3. Assume that the price of the output is 3. Suppose the size of the market is limited and only 4 units can be sold at most. Answer the following: (A) Is this business viable? Use math to justify your answer. (B) Give an example of a business that can be represented by this function. Justify why you think this function appropriately models it. Hints: Look at other problems you solved. Find the break-even point. Find where minimized costs equals total revenue. You will need costs and revenue as a function of Q. Use the break even to assess whether this business is a good option. Think about what x could mean.X and Y are both factors of production. X's marginal product is 30 and Y's is 20. X is $5 each and Y is $4 each. Knowing that Y costs less than X, we can assume that the firm will make the same output at a cheaper cost by using less of X and more of L. Is this statement true or false? Explain.
- In long-run equilibrium, suppose that this restaurant charges $11 per meal for 180 meals and that the marginal cost of the 180th meal is $9. Suppose that the allocatively efficient output level in long-run equilibrium is 200 meals. What is the firm's profit? (Please note that $360 and $180 are not the correct answers) $ ?Suppose a firm faces a cost function of C = 8 + 4q + q^2, so that its marginal cost is MC=4 + 2q. a) What is the firm's fixed cost. F? b) What is the formula for the firm's variable cost (VC), Average Cost (AC), and Average Variable Cost (AVC)? c) On a diagram, draw the AC, AVC, and MC curves.State the relationship between average product (AP)and marginal profit (MP) when AP is increasing, is AP above (greater), below (less) or equal to MP? ________ chose one AP is decreasing, is AP above, less or equal to MP? _________ choose one AP is maximum, Is AP above, less of equal to MP? _____________ choose one