For the next three problems, consider 1.0 L of a solution which is 0.6 M HC₂H₃O₂ and 0.2 M NaC₂H₃O₂ (K_a for HC₂H₃O₂ = 1.8 x 10^-5). Assume 2 significant figures in all of the given concentrations so that you should calculate all of the following pH values to two decimal places.

1. Calculate the pH of this solution.

2. Calculate the pH after 0.10 mol of HCl has been added to the original solution. Assume no volume change on addition of HCl.

3. Calculate the pH after 0.20 mol of NaOH has been added to the original buffer solution. Assume no volume change on addition of NaOH.

6) The Crescent Street Jam (a local jazz quintet, with your Professor on Piano) has market power. Consumers in Potsdam demand tickets to each (monthly) live performance according to P=18-0.2*Q (MR=18-0.4Q). The band faces a constant Marginal Cost of MC=$0.10. Their total costs are TC=150+0.1Q

a) In this setting, how many tickets should they sell to each concert to maximize profits? At what price should those tickets be sold? What are the band’s profits? Graph this scenario.

b) What would be the band’s profits if they could use 1st Degree (Perfect) price discrimination? Graph this scenario.

c) Suppose that since the band has twice monthly performances (24 per year), they choose to use block/quantity pricing to sell “season” ticket packages to individuals. A ticket can then be used for ANY of the 24 concerts in a year. Suppose individual consumers have an annual demand for tickets represented by P=6-0.2*Q. How much should the band charge for a bundle of tickets and how many tickets should be in each bundle, again assuming that MC is constant at $0.10? Graph this scenario.

d) The bar where they band plays sells Yuengling Beer. When the band is performing each consumer’s demand for Yuengling is P=8-1.5B, where B represents the quantity of beer consumed. The bar’s marginal cost is $0.50. The bar can use two-part pricing by charging a “cover” charge. How large should the cover charge be? How much should the bar charge for each beer? Graph this scenario.

Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes.

Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions.

a. Calculate the expected rate of return on each alternative.

b. Calculate the standard deviation of returns on each alternative.

c. Calculate the coefficient of variation on each alternative.

d. Calculate the beta on each alternative.

A corridor connecting a suburban region to the Central Business District (CBD) is experiencing significant congestion during morning peak periods. The primary purpose of travel during the peak period is “work”, and the corridor has two main modes-drive alone (single occupant vehicle=SOV), and carpool. The city transportation engineer is considering converting a lane in each direction of travel into a high occupancy vehicle (HOV) only lane. The city officials want 2 to know what impact this proposed measure would have on current mode split in the corridor. A multinomial logit model is to be used for the analysis. The utility functions for the model are:

V_SOV = 2.0 - 0.05( TT_SOV) - -0.2 (TC _SOV)

V_carpool = - 0.05(TT_Carpool) - 0.2(TC _Carpool)

TTi=travel time by mode i, minutes TCi=travel cost by mode i, dollars

Carpool =2-person carpool

Assume 2-person carpool cost is half cost for single occupant vehicle in the base condition only

The current count of vehicles in the corridor based on vehicle occupancy is:

Number of single occupant vehicles=3268

Number of 2-person carpool vehicles=532

The expected system attribute values if the HOV lane were to be implemented are:

TT_auto = 20 minutes

TT_carpool = 12 minutes

TC_auto = $7.75

TC_carpool = $3.75

i. Determine what the current mode split is in the corridor

ii. Determine what the current average car occupancy is in the corridor.

iii. Determine what the expected mode split would be after implementation of the HOV lane.

iv. Determine what the expected average car occupancy in the corridor would be after implementation of the HOV lane.

A corridor connecting a suburban region to the Central Business District (CBD) is experiencing significant congestion during morning peak periods. The primary purpose of travel during the peak period is “work”, and the corridor has two main modes-drive alone (single occupant vehicle= SOV), and carpool. The city transportation engineer is considering converting a lane in each direction of travel into a high occupancy vehicle (HOV) only lane. The city officials want 2 to know what impact this proposed measure would have on current mode split in the corridor. A multinomial logit model is to be used for the analysis. The utility functions for the model are:

VSOV = 2.0 - 0.05( TTSOV) - -0.2 (TC SOV) Vcarpool = - 0.05(TTCarpool) - 0.2(TC Carpool)

TTi=travel time by mode i, minutes TCi=travel cost by mode i, dollars

Carpool =2-person carpool

Assume 2-person carpool cost is half cost for single occupant vehicle in the base condition only

The current count of vehicles in the corridor based on vehicle occupancy is:

Number of single occupant vehicles=3268

Number of 2-person carpool vehicles=532

The expected system attribute values if the HOV lane were to be implemented are:

TTauto = 20 minutes TTcarpool = 12 minutes TCauto = $7.75 TCcarpool = $3.75

i. Determine what the current mode split is in the corridor

ii. Determine what the current average car occupancy is in the corridor.

iii. Determine what the expected mode split would be after implementation of the HOV lane.

iv. Determine what the expected average car occupancy in the corridor would be after implementation of the HOV lane.

A colleague of yours from the GIMPA School of Technology has decided to venture into Sobolo production and as a student of Managerial Economics, he/she has pleaded with you to help boost demand and revenue. You estimated that the demand equation for his or her Sobolo is: ??=50−0.5??+0.2?+0.5???+1.25? where Qs is the number of 500ml bottles of Sobolo demanded, Ps is the price he/she charges per 500ml bottle of Sobolo, I is the average income per month of his or her customers and Pos is the price his or her closest competitors charge per 500ml bottle of Sobolo and A is your colleague’s investment in marketing or advertisement campaign: a) Interpret the demand equation and explain what might have informed your choice of these factors as key determinants of Sobolo demand and why? b) Suppose that your colleague sold 350 bottles of Sobolo last week, where I = GHc 1,500, Pos = GHc 2.00 with no investment in advertisement, what is the price (Ps) that your colleague charged per bottle of Sobolo? Find and explain the price and income elasticities of demand for Sobolo. c) Your colleague is considering a GHc 1,100 promotional campaign to bolster sales and revenues and you have projected that the promotional campaign will change the demand equation to: ??=55−0.5??+0.2?+0.5???+4.25? Supposing that your projections are accurate, what number of bottles of Sobolo (Qs) will your colleague sell and why based on ?? , ? and ??? info in b? d) How will the concept of opportunity cost help you establish whether your colleague’s promotional campaign will be effective or not given no change in average income of his or her customers and no change in price of his or her closest competitors? What is advertisement elasticity of demand for Sobolo?

A 2010 Pew Research poll asked 1,306 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies. Earth is warming Not warming Don't know (or refuse) Total Conservative Republican 0.11 0.2 0.02 0.33 Mod/Lib Republican 0.06 0.06 0.01 0.13 Mod/Cons Democrat 0.25 0.07 0.02 0.34 Liberal Democrat 0.18 0.01 0.01 0.2 Total 0.6 0.34 0.06 1 a) Are believing that the earth is warming and being a liberal Democrat mutually exclusive? not mutually exclusive mutually exclusive b) What is the probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat? (please round to four decimal places) c) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a liberal Democrat? (please round to four decimal places) d) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a conservative Republican? (please round to four decimal places) e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party ideology? belief in global warming and party ideology are dependent belief in global warming and party ideology are independent f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that he does not believe that the earth is warming? (please round to four decimal places)

A corridor connecting a suburban region to the Central Business District (CBD) is experiencing significant congestion during morning peak periods. The primary purpose of travel during the peak period is “work”, and the corridor has two main modes-drive alone (single occupant vehicle= SOV), and carpool. The city transportation engineer is considering converting a lane in each direction of travel into a high occupancy vehicle (HOV) only lane. The city officials want 2 to know what impact this proposed measure would have on current mode split in the corridor. A multinomial logit model is to be used for the analysis. The utility functions for the model are:

VSOV = 2.0 - 0.05( TTSOV) - -0.2 (TC SOV) Vcarpool = - 0.05(TTCarpool) - 0.2(TC Carpool)

TTi=travel time by mode i, minutes TCi=travel cost by mode i, dollars

Carpool =2-person carpool

Assume 2-person carpool cost is half cost for single occupant vehicle in the base condition only

The current count of vehicles in the corridor based on vehicle occupancy is:

Number of single occupant vehicles=3268

Number of 2-person carpool vehicles=532

The expected system attribute values if the HOV lane were to be implemented are:

TTauto = 20 minutes TTcarpool = 12 minutes TCauto = $7.75 TCcarpool = $3.75

i. Determine what the current mode split is in the corridor

ii. Determine what the current average car occupancy is in the corridor.

iii. Determine what the expected mode split would be after implementation of the HOV lane.

iv. Determine what the expected average car occupancy in the corridor would be after implementation of the HOV lane.