Problem Set 2 This is where I’m totally lost—I’m not even sure how to begin these problems.

1. Anne is currently renting an apartment for $800 per month. Assume each dollar buys “1 unit of housing.”

a. Draw a sample budget line (with housing as one good and everything else as the other good) and indifference curve that shows Anne’s current consumption.

b. Suppose that Anne qualifies for a government housing program that will provide her, at no cost, an apartment that is $600/month or less. She cannot supplement this expenditure on housing (for example she can’t spend another $200 to get her current apartment). Show graphically how this affects her budget constraint.

c. Show how Anne’s decision whether to take advantage of this program depends on the shape of her indifference curves.

d. Suppose instead, that the government gave Anne $600 instead of an apartment. How would this affect her overall utility?

2. Draw a set of indifference curves for the following pairs of goods:

a. Hamburgers and carrots for a vegetarian who neither likes nor dislikes meat. (Vegetarians do not eat meat.)

b. Peanut butter and jelly for an individual that will not eat peanut butter sandwiches or jelly sandwiches, but loves peanut butter and jelly sandwiches made with two parts peanut butter and one part jelly.

c. Tickets for Knott's Berry Farm (KBF) and Universal Studios (US) for a tourist that believes that KBF and US are perfect substitutes.

3. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3 ∙ XY2. The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500.

a. Sketch a set of two indifference curves for Sally in her consumption of X and Y.

b. Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope.

c. Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. Show her optimum point on a graph. (Partial units for the quantities are possible.) (Note: MUY = 6XY and MUX = 3Y2.)

d. Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What would happen to her utility as a result of the price increase?

Problem Set 3

1.  In problem set #1 the demand for cigarettes was given as QD = 658 – 94P and the supply was given as QS = 235 +117.5P.

a.  Calculate the consumer surplus at the equilibrium price of $2 per pack.

b.  Some of you suggested that supply of cigarettes should be limited. Let’s assume the supply is limited to 300 billion cigarettes/year. Calculate the consumer surplus now (note the demand and supply curves do not change, the new price will be given by the demand for cigarettes at the quota level).

c.  Others suggested that we try to change preferences by advertising the health effects of cigarettes. Suppose we are successful in this endeavor and the demand curve becomes QD = 500-148P. What is the consumer surplus at our new equilibrium.

1: I thought I had calculated these correctly, but in each case it seems my professor had used and calculated different figures. In both cases, the differences started with the y-intercept—am I wrong to use the figure straight from the demand equation? (as in y=mx+b, then b is the y-intercept, or if Qd= 658-95P then 658 is the y-intercept?)

Here are my figures vs. his:

a)  I said: CS=.5(656)(470) Prof said: CS=.5(7-2)(470).

It looks like instead of 658 he just rounded up the y-intercept to 7?

c)  I said: CS=.5(500)(352) Prof said: CS=.5(3.7-1)(352)

For the life of me I cannot figure out where the y-intercept of 3.7 is coming from.

I understood question 2, but I was lost on how to begin question 3.

3. The demand for taxi rides in New Brunswick can be segmented into components, the demand from residents and the demand from visitors. The demand from residents is given by:

Qr = 1700 – 250 P

The demand from visitors is given by (where P= $/mile)

Qv = 2500 - 2000P

a. What is the total market demand curve (show both algebraically and graphically)

b At a market price of $1 what is the total consumer surplus, the consumer surplus for residents, and the consumer surplus for visitors?

c. Calculate the elasticities of demand for residents and visitors at a price of $1. Who will cut back their taxi usage more if prices increase?

Problem Set 4

1: I was able to get most of this question successfully

a) I could graph R, TC, and profit but stumbled on ATC/AVC. How do I calculate those given the information provided?

b) 500K (intersection of TC and profit on my graph)

c) MC=.00002Q, MC=.00002(500,000), MC=10. I got this right, but I guess I’m not entirely sure how/why this verifies the answer to b? Is it because the company is selling the milk at $10 a container?

d) I was lost here, but came up with this table for partial credit:

Units / TC / Profit
400k / 2mil / 2
500k / 3mil / 2
600k / 4.2mil / 1.8

1. Seth’s Soy Milk Company produces soy milk that sells for $10 a container. Seth’s total cost curve is given by:

TC = 90,000 + 0.00001Q2

Where Q is containers per year.

a.  Graph TC, AC, AVC, revenue, and profit vs. Q. (hint: vary Q from 100,000 to 1,000,000 by 100,000s)

b.  From your graph determine how much soy milk Seth should produce.

c.  The Marginal cost of formula is given by:

MC = 0.00002Q.

Verify your answer to part b.

d.  If the government imposes a tax of $1/container on Seth how will this affect the amount he produces and his profit? (His TC function changes to 90,000 + Q +.00001 Q2 and his MC changes to 1+ 0.00002Q)

2: a) 120kl/60k2=15/7.5 > 900k2=900kl > k=l, so 1:1 ratio

b) I’m not sure how to calculate this in the intended/right way, but I got 44 employee hours through trial and error.

c-e) This is where the wheels fell off again and I was totally lost.

2. Noah’s Fried Chicken Restaurant has an annual production function of :

60K2 L

where K is the number of kilowatts/hour used by chicken frying machines and L is the number of hours per day worked by employees. The marginal products are

MPK = 120KL

MPL = 60K2

It costs Noah $7.50/hour to pay his employees and $15/kilowatt/hour to run his chicken machines.

a. Find the optimal ratio of kilowatts/hour to employee hours.

b. If Noah’s daily budget is $1000 how many employee hours per day should he hire for?

c.  Calculate the total product, marginal product of labor, the average product of labor. Calculate the marginal cost of labor at this production level (assume that employees work 2000 hours/year).

d.  If a living wage of $10/hour is enacted how many hours will Noah now need to hire for

e. Repeat the calculations of part c. for the new conditions.