如果将例2中两产品厂商的需求函数和成本函数改为如下:求满足利润最大化的产出水平及其最大利润

如果特例2中两产品广商的需求函数和成本函数改为如下，

求满足利润最大化的产出水平Q₁和Q₂及其最大利润.

一家企业的固定生产成本为5000美元，边际生产成本为常数，为500美元/单位产品。

(1)企业的总成本函数是什么？平均成本呢？

(2)如果企业想使其平均总成本最低，它应该选择非常大的产量还是比较小的产量？解释你的结论。

A firm has a fixed production cost of $ 5000 and a constant marginal cost of production of S 500 per unit produced.

a. What is the firm' s total cost function？ Average cost？

b. If the firm wanted to minimize the average total cost，would it choose to be very large or very small？ Explain.

下表显示了一个以常数边际成本10美元生产的垄断者面临的需求曲线。

(1)计算该厂商的边际收益曲线。

(2)该厂商的利润最大化产量和价格是多少？该厂商的利润为多少？

(3)在一竞争性行业中均衡价格和数量各为多少？

(4)如果该垄断者被迫以完全竞争的均衡价格生产，社会得益是什么？结果是谁获益谁受损？

The following table shows the demand curve facing a monopolist who produces at a constant marginal cost of $ 10.

a. Calculate the firm' s marginal revenue curve.

b. What are the firm's profit - maximizing output and price？ What is its profit？

c. What would the equilibrium price and quantity be in a competitive industry？

d. What would the social gain be if this monopolist were forced to produce and price at the competitive equilibrium？ Who would gain and lose as a result？

一家竞争性厂商的短期成本函数如下:

C(q)=q³-8q³+30q+5

(1)求出MC、AC和AVC,并在图形上表示出来。

(2)当价格位于哪一区间时厂商产量为零？

(3)在图上标出厂商的供给曲线。

(4)当价格为多少时企业产量为6？

A competitive firm has the fallowing short - run cost function: C(q)=q³-8q²+30q+5.

a. Find MC, AC, and AVC and sketch them on a graph.

b. Al what range of prices will the firm supply zero output？

e. Identify the firm's supply curve on your graph.

d. At what price would the firm supply exactly 6 units of output？

(1)如果公司决定将两种产品的价格都提高10%，其销售量会有什么变化？销售收入呢？

(2)你能否从已知的信息中判断，哪个产品会给厂商带来最大的收入？如果答案是肯定的，为什么？如果无法做出回答，你还需要哪些信息？

The ACME Corporation determines that at current prices the demand for its computer chips has a price elasticity of-2 in the short run, while the price elasticity for its disk drives is- 1.

a. If the corporation decides to raise the price of both products by 10 percent , what will happen to its sales？ To its sales revenue？

b. Can you tell from the available information which product will generate the most revenue for the firm？ If yes, why？ If not, what additional information would you need？

1983年里根执政时，推行"实物支付计划"。以小麦市场为例，考察该计划如何奏效。

(1)假设需求函数为Q^D=28-2P，供给函数为Q^S=4+4P。P是小麦的价格，单位为美元/蒲式耳，Q是产量，单位为10亿蒲式耳，试求出自由市场均衡价格和产量。

(2)假设政府向农民支付小麦，鼓励农民将部分土地退耕，使供给减少自由市场均衡量产量的25%。用于支付的小麦来源于政府储备，数量等于退耕土地的收获量。农民可在市场上自由出售这些小麦。问农民的产量为多少？政府间接供应市场多少小麦？新的市场价格是多少？农民获益多少？消费者得益还是受损？

(3)如果政府不把小麦返送给农民，小麦将积压或变质。纳税人从该计划中受益吗？该计划存在什么潜在问题？

In 1983, the Reagan Administration introduced a new agricultural program called the Payment-in-Kind Program. To see how the program worked, let' s consider the wheat market.

a. Suppose the demand function is Q^D=28-2P and the supply function is Q^S=4+4P, where P is the price of wheat in dollars per bushel and Q is the quantity in billions of bushels. Find the free-market equilibrium price and quantity.

b. Now suppose the government wants to lower the supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollars- hence the name of the program. The wheal comes from the government ' s vast reserves that resulted from previous price support programs. The amount of wheal paid is equal to the amount that could have been harvested on the land withdrawn from production. Farmers. are free to sell this wheat on the market. How much is now produced by farmers？ How much is indirectly supplied to the market by the government？ What is the new market price？ How much do the farmers gain？ Do consumers gain or lose？

c. Had the government not given the wheat back to the farmers, it would have stored or destroyed i. Do taxpayers gain from the program？ What potential problems does the program create？

如例1图(a)所示,试将等腰梯形AB-CD中阴影的面积S表示成x(0≤x≤a)的函数.

某公司的短期总成本函数由等式TC=200+55q给出，式中，TC为总成本; q为总产出数量;两者均以千计。

(1)该公司的固定成本是多少？

(2)如果该公司生产了100000单位的产品，它的平均可变成本是多少？

(3)其所生产的单位产品的边际成本是多少？

(4)其平均固定成本是多少？

(5)假定该公司通过贷款扩大生产规模，其固定成本增加5000美元，但其可变成本降至每1000单位产品45000美元，利率i也进入成本函数。利率每上升1%，成本增加3000美元。写出新的成本函数。

The short - run cost function of a company is given by the equation TC = 200 +55q, where TC is the total cost and q is the total quaintly of output ，both measured in thousands.

a. What is the company' s fixed cost？

b. If the company produced 100000 units of goods, what is its average variable cost？

c. What would be its marginal cost of production？

d. What would be its average fixed cost？

e. Suppose the company borrow money and expands its factory. Its fixed cost rises by

$ 50000, but its variable cost falls to $ 45000 per 1000 units. The cost of interest (i) also enters into the equation. Each one-point increase in the interest rate raises costs by $ 3000. Write the new cost equation.