3.Consider a coffee shop that has two types of customers: lawyers and doctors. The demand for espresso by lawyers is given by QL= 18 –3P, where P Is measured in dollars and Q Is measured in ounces. The demand for espresso by doctors is given by QD= 10 –2P. There are equal numbers of lawyers and doctors. The marginal cost of an ounce of espresso is $2. (a)Suppose that the coffee shop can identify which customer is a doctor and which is a lawyer. The shop will offer each type of customer a specific size cup of espresso for some total price. How many ounces of espresso will lawyers be offered, and at what total price? How many ounces of espresso will doctors be offered, and at what total price? (HINT: you should find that lawyers are offered a 12 ounce drink for $48, and doctors are offered a 6 ounce drink for $21. Lawyers and doctors are both tired and rich!) (b)Suppose that the shop owner can no longer distinguish the lawyers from the doctors (e.g., the doctors don’t put on their white coats before getting their espresso).Suppose the shop still offers the two options you found in part (a). That is, each customer has the option of paying $21 for 6 ounces or $48 for 12 ounces. How will the customers respond? (c)Keeping the drink sizes the same (6 ounces and 12 ounces), how should the coffee shop owner change the total prices of the two drinks so that lawyers will buy the lawyer option and doctors will buy the doctors option, and profits are maximized? (d)Describe qualitatively how the coffee shop owners should change the drink sizes (and then the prices) to increase profits even further, while still ensuring that lawyers will buy the lawyer option and doctors will buy the doctors option. (e)Suppose that the coffee shop owner could only charge a single, uniform two-part tariff to all customers. That is, both lawyers and doctors pay the same cover charge Cand per-ounce price p. Describe qualitatively what C and p should be if the shop owner maximizes profits. Can you put upper and / or lower bounds on Cand/or p?

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3. Calculate th elasticity of substitution for the production function

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3.Ballreich’s has observed that quantity of values in a town increases from 20000 bags per week to 24000 bags per week where it increases advertising expanding from $32000 to $33000. It has also in the market that the number of sales increases from 12000 to 13000 bags per week when its competitors raise their prices from 3.50 per bag to 3.75 per bag( while their advertising remain consistent) A. Ballreich’s knows that the price of electricity demand is 4.7 . If Budweiser increased their advertising by 10% and increased prices by 15%. By what percent would the quantity of sales change ? Short Answer Apply:

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3. An oil company contemplates investing 100 million dollars per year (in constant dollars) for five years in exploratory work to confirm the existence of new exploitable reserves. It will then face a potential delay until market conditions justify exploitation, which will require investing 200 million dollars for three years in production facilities, following which delivery of oil can start with a projected net revenue of 100 million dollars per year, essentially ad infinitum.

a. At a real discount rate of 5%/yr what is the longest delay tolerable between the start of exploitation and the start of oil delivery: i.e., how far in advance is it worth proving out reserves?

b. If the real discount rate were 10%/yr, what is the maximum time delay?

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3. A new large scale senior community isbeing developed, and one of the decisions to be made is where to locate the twofire stations that have been allocated to the community. For planning purposes, the community has beendivided into five tracts, with no more than one fire station to be located inany given tract. Each station is torespond to all of the fires that occur in the tract in which it is located aswell as in the other tracts that are assigned to this station. The followingtable gives the average response time (in minutes) to a fire in each tract (thecolumns) if that tract is served by a station in a given tract (the rows). The bottom row gives the forecasted average number of fires that willoccur in each of the tracts each year. Formulate this problem situation as an integer programming model.

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