Section A

1.Suppose that an individual with income I cares about two goods, X and Y . The price of the two goods is pX and pY . The individual has the following utility function: U(X,Y)=X^0.5 +Y^0.5

(a) Find the optimal consumption bundle by solving the utility maximization problem.

(b) Find the indirect utility function.

Joseph likes coffee (C) twice as much as tea (T), and views a cup of coffee as a perfect substitute to two cups of tea. The price of a cup of coffee is $3, the price of a cup of tea is $2, and Joseph has $30 to spend on hot beverages.

(a) Write down a utility function that represent Joseph's preferences.

(b) How much of each drink will Joseph buy? (Hint: the first order conditions will not help; draw the indifference curves and the budget constraint and think about what you would do in this situation.)

(c) Now, suppose that the price of a cup of coffee rises to $5. How does the consump- tion of Joseph change?

(d) What is Joseph's demand for coffee and tea as a function of prices and income {pC,pT,I}? You will have three cases depending on the relationship between pC and pT .

3.

Britney eats peanut butter (P) and jelly (J) on her toast every morning. She likes her toasts with twice as much jelly as peanut butter. Therefore, when she buys a jar of peanut butter, she also needs to buy two jars of jelly to match that peanut butter and vice-versa. So, she views two jars of jelly as a perfect complement to one jar of peanut butter. The price of P is $1, the price of J is $3, and she has $28 to spend.

(a) Write down a utility function that represents Britneys preferences over peanut butter and jelly jars.

(b) How much peanut butter and jelly jars is she going to consume? (Hint: the first order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that has a point in common with the budget constraint).

(c) What is the exact value of Britney's indirect utility?

Section B.

2) If the price of automobiles were to increase substantially, the demand curve for gasoline would most likely

A) shift leftward. B) shift rightward.

C) become flatter. D) become steeper.

3) If the price of automobiles were to decrease substantially, the demand curve for automobiles would most likely

A) shift rightward. B) shift leftward.

C) remain unchanged. D) become steeper.

4) Suppose a market were currently at equilibrium. A rightward shift of the demand curve would cause

A) an increase in price but a decrease in quantity.

B) a decrease in price but an increase in quantity.

C) an increase in both price and quantity.

D) a decrease in both price and quantity.

5. Draw out examples of each of the following indifference curves: imperfect substitutes, perfect substitutes, and perfect complements.

6) If two bundles are on the same indifference curve, then

A) the consumer derives the same level of utility from each.

B) the consumer derives the same level of ordinal utility from each but not the same level of cardinal utility.

C) no comparison can be made between the two bundles since utility cannot really be measured.

D) the MRS between the two bundles equals one.

7) The consumer is in equilibrium when

A) MRT = MRS.

B) Px/Py = MUx/MUy.

C) the budget line is tangent to the indifference curve at the bundle chosen.

D) All of the above.

8. Jody enjoys having exactly 1 teaspoon of sugar with every cup of coffee she has. What does this say about her indifference curves between the two goods? What happens to her utility level when she is given 5 teaspoons of sugar with one coffee? (Just an explanation)

9) Jay's Utility function is given by U(x,z) = 3x10.2 x20.8 and P1=$2 and P2=$4 and his budget is $200.

Write out the Lagrange but don't solve it

Find the utility maximizing values of x1 and x2

10)What does the substitution effect cause a consumer to do if the price of a good increases?

11) What does the income effect cause a consumer to do if the price of a good increases? What else is needed here?

12) What can we say about the substitution and income effects on a decrease in wages? What is an Engel curve and how does it relate here? If leisure is viewed as an inferior good, how would the labor demand curve look?

13) Suppose m=120, p1= 5, and p2=6.

What is the budget equation?

What is the slope of the budget line?

How does the budget set change with the following:

a 20% increase in m

a 2$ decrease in p2.

Part c.

11.2. A monopolist faces a market demand curve given by Q = 3'0 P. The monopolist's marginal revenue function is given by MR 2 2m 2Q. a. If the monopolist can produce at constant average and marginal costs of AC = MC 2 6, what out put level will the monopolist choose in order to maxi- mize prots? What is the price at this output level? 'What are the monopolist's prots? b. Assume instead that the monopolist has a cost structure where total costs are described by TC = 0.25:? SQ + 300 and marginal cost is given by MC = 0.5Q 5. With the monopolist facing the same market demand and marginal revenue, what pricequantity combination will be chosen HOW to maximize prots? What will prots be? c. Assume now that a third cost structure explains the monopolist's position, with total costs given by 1] TC: c.0103 Q2 +45Q+1o and marginal costs given by MC = 0.03632 2Q + 45. Again, calculate the monopolist's price-quantity combination that maximizes prots. What will prots be? (Hint: set MC 2 MR as usual and use the quadratic formula or simple factoring to solve the equation for Q.) (1. Graph the market demand curve, the MR curve, and the three marginal cost curves from part a, part b, and part c. Notice that the monopolist's prot-making ability is constrained by (1} the mar- ket demand curve it faces (along 1vvith its associated MR curve), and (2} the cost structure underlying its In reporting on real GDP growth in the second quarter of 2016, an article on Reuters news noted that: "U.S. economic growth unexpectedly remained tepid in the second quarter as inventories fell" and also that the "inventory drawdown was almost across the board." Source: Lucia Matikani, "Inventory Reduction Curbs U.S. Economic Growth; Rebound Expected," reuters.com, July 20, 2016. If companies are drawing down inventories is aggregate expenditure likely to have been larger or smaller than GDP? O A. Smaller than GDP, because more is being bought than produced. O B. Larger than GDP, because less is being bought than produced. O C. Larger than GDP, because more is being bought than produced. O D. Smaller than GDP, because less is being bought than produced. The chief economist at UniCredit Research is quoted in the article as stating that: "The U.S. economy just went through a meaningful inventory correction cycle." What would an "inventory correction cycle" be? O A. A situation where companies deplete low levels of inventory to earn economic profits. O B. The process of companies increasing production levels to create more inventory. O C. A situation where inventory levels are held constant for stability. O D. The process of companies decreasing or increasing actual inventories to match planned inventories. The article states that: "Though the inventory drawdown weighed on GDP growth, that is likely to provide a boost to output in the coming quarters." Why would an inventory drawdown boost output in the coming quarters? O A. Once the firms are able to sell off their excess inventories, consumption will be lower. O B. Once inventories reach desired levels, firms will increase production to match expected planned aggregate expenditures. O C. This would indicate that the quantity of output demanded is greater than the quantity of output supplied, and production levels will rise. O D. An inventory drawdown would reduce storage costs, thus giving firms an incentive to produce more output