1.[9 pts]Consider a company who knows that the demand curve that they face for their product can be described by P=20-0.2Q. Their marginal cost of production is constant at $4 per unit.

1. [3 pts]Determine the equation for their marginal revenue as a function of the quantity sold. Sketch a plot showing their inverse demand curve, marginal revenue curve, and marginal cost curve all on one plot.
2. [3 pts]What price should they set to maximize their profit? How much profit (ignoring fixed costs) do they make at this price?
3. [3 pts]If they produce and sell one more unit than the quantity you determined in part (b), what will their profits be? If they produce and sell one less unit than the quantity you determined i part (b), what will their profits be?

3.[6 pts] Washtenaw County is looking to repave a large number of roads and puts out a Request For Proposal (RFP) looking for contractors to do the work. Specifically, the city is looking to repave 700 miles of road, and is willing to hire multiple contractors to do the work. (I.e., one contractor doesn't have to be willing/able to repave all 700 miles in order to win some of the work.) In the RFP, the county states that they will pay all contractors a standard rate of $120,000 per mile paved. (Or the pro-rated amount per portion of a mile.)

Peter and Lois run a paving company and are thinking of bidding to win some of this work. Their company's marginal cost for paving a road is given by MC(q)=100,000+400q, whereqis the number of miles of road paved. (This means that the marginal cost ofq=1 is $100,400. The marginal cost ofq=2 is $100,800. Etc.)

1. [3 pts]Suppose there are no additional fixed costs that Peter and Lois would incur related to this opportunity. How many miles of road should Peter and Lois bid for (i.e., agree to supply)?
2. [3 pts]Suppose now that there are additional fixed costs ofFdollars to be incurred if Peter and Lois are to bid for this business. What is the highest value ofFfor which they would still find it worthwhile to bid? (Hint: If you are trying to calculate an area here, you are probably doing it correctly. However, no calculus is necessary! Draw the picture.)

4.[10 pts]TruePoo is a small startup company that sells Shampoo in the Detroit area. They currently are pricing each bottle of shampoo at $18 a bottle. Historical they have sold about 600 bottles of shampoo each week. The CEO hires you out of business school to help improve the profitability of the company. You need to understand both their production costs and their demand curve.

1. [2 pts]After interviewing managers and examining the accounting books, you discover that the company pays $400,000 per year in salaries and benefits (which are paid unrelated to the amount of shampoo sold), and $5,000 per month in rent on their factory in Detroit. Their marketing and advertising costs, which is determined at the beginning of each quarter before actual production is known, averaged out last year to $3.20 per bottle sold. They pay $0.30 for each plastic bottle the shampoo is packaged in, and $1.70 for the chemicals used in each bottle of shampoo. Last year they also paid a graphic design firm $20,000 to re-imagine their branding and redesign the logos on their bottles. What is their marginal cost of production for each bottle of shampoo?
2. [4 pts]Having understood cost, you now set out to understand the demand curve. To do so, you convince the CEO to run an experiment where they lower the price of the shampoo from $18 per bottle to $16 per bottle for a few weeks. You specifically pick weeks to run this experiment when you are comfortable assuming that nothing else major about the market changed. During the price experiment, the company sells, on average, 700 bottles per week. (i) What is the company's own-price elasticity of demand (at initial price of $18 per bottle)? (ii) What is the profit maximizing price? (Note: You can assume that the demand curve is always linear.)
3. [4 pts]Suppose that, due to a supply chain issue in the chemicals industry, the cost to purchase the chemicals needed to make shampoo increases by 20%. Assuming nothing else changes, what is now the profit maximizing price? Did your profit-maximizing price go up one-for-one with the change in cost? Briefly give an intuitive explanation.

5.[9 pts]You are a consultant who specializes in providing advice to firms with monopoly power. Three single-price monopolist firms (from different markets) are currently seeking your advice. Although the information they have supplied to you, summarized in the table below, is incomplete, your expert knowledge of economics may allow you to make a recommendation in each case.

For each firm, make a recommendation for what they should do in the short-run, selecting from one of the following options.

• remain at the current output level
• increase output
• reduce output
• shut down
• go back and recheck the figures because the ones supplied cannot be right

To get full credit you must also justify your answer.

	Firm A	Firm B	Firm C
Current price	24	6	30
Marginal revenue	16	6.10	25
Total revenue	12,000	3,000	6,000
Total cost	11,500		9,500
Marginal cost	16	4.50	23
Average total cost	23	4.10
Average variable cost	21	4.20	28

1. [3 pts]Give your recommendation and justification to Firm A.
2. [3 pts]Give your recommendation and justification to Firm B.
3. [3 pts]Give your recommendation and justification to Firm C.

6.[10pts] Consider a farmer that grows both corn and soybeans. Both of these products are commodities that are bought & sold in highly competitive markets and so our individual farmer has no real control over the price at which she sells her products.

Suppose that the current market price of corn is $3.70 per bushel and the current market price of soybeans is $8.75 per bushel. The farmer's marginal cost of production of corn is MC=0.005q_cornand her marginal cost of production of soybeans is MC=0.014q_soy. (In both equations, q is measured in bushels.) The fixed cost of growing and harvesting corn is $1000, and the fixed cost of growing and harvesting soybeans is $800. (Suppose that the farmer has enough land such that she could grow as many bushels of either product as she wants.)

1. [3 pts]A farming consultant tells the farmer: "The price of soybeans is higher than the price of corn. Therefore, in order to maximize profit you should produce more soybeans than corn." Do you agree or disagree and why? (Note: To "explain why" it is not good enough to just state the answer to part (c) of this question. You should try to give some sort of intuitive/more general reason why the statement is true or false.)
2. [3 pts]True or false (and explain why): "In addition to the price of soybeans being higher, the fixed cost of harvesting soybeans is smaller. So you shoulddefinitelygrow more soybeans than corn."
3. [4 pts]What are the profit maximizing quantities of each product that the farmer should grow? What will her total profits be? Which crop is more profitable? Given that one crop is more profitable than the other, why doesn't she increase her production of that one and decrease her production of the less profitable crop?