Week 2 Microeconomics Practice Questions PDF

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Week 2 Microeconomics Practice QuestionsChapter 3Review Question 3. Describe the equal marginal principle. Explain why this principle may not hold if increasing marginal utility is associated with the consumption of some goods.Equal marginal principle: Take a utility function U(X,Y) with smooth conv...

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Week 2 Microeconomics Practice Questions Chapter 3 Review Question 3.11! Describe the equal marginal principle. Explain why this principle may not hold if increasing marginal utility is associated with the consumption of some goods.! Equal marginal principle:! • Take a utility function U(X,Y) with smooth convex indifference curves. ! • At the optimal choice MUx/Px = MUy/Py!

! If MUx and MUy are increasing:! • Consuming more X increases MUx/Px. If this is larger than MUy/Py, then consumers should keep spending more on X and less of Y —> corner solution (=equal marginal principle doesn’t need to hold at a corner solution)!

Exercise 3.14 a,b,d! Connie has a monthly income of $200 that she allocates between two goods: meat and potatoes.! a) Suppose meat costs $4 per pound and potatoes $2 per pound. Draw her budget constraint.! Given: !

Her budget constraint:!

If she buys no meat (M=0); ! 4(0)+2P=200! 2P=200! P=100! If she buys no potatoes (P=0)! 4M+2(0)=200! 4M=200! M=50!

b) Suppose also that her utility function is given by the equation U(M,P)=2M+P. What combination of meat and potatoes should she buy to maximize her utility?! We already have the budget constraint: 4M + 2P = 200 ! ! Solve the budget constraint for M

$ $

! —> M = 50 -0.5P!

Utility function: U = 2M +P. Also linear! ! Solve the utility function for M; !

!

—> M = 0.5U-0.5P!

The budget constraint and the indifference curves have the same slope: -0.5.! —> One of the indifference curves coincides with the budget line, this means that that indifference curve is where the consumer would maximize her utility. ! Any combination of M & P on the budget line;! M = 50 - 0.5P maximizes her utility!!

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c) An outbreak of potato rot raises the price of potatoes to $4 per pound. The supermarket ends its promotion. What does her budget constraint look like now? What combination of meat and potatoes maximizes her utility?! New Budget constraint:! $ 4M + 4P = 200! Solve Budget constraint for M:

$ —> M = 50 - P! The slope is -1! Utility function: U = 2M +P. Also linear! ! Solve the utility function for M;

$ —> M = 0.5U-0.5P! The slope is -0.5! The budget constraint is steeper than the indifference curves: |-1| > |-0.5| ! —> A corner solution: (P*, M*) = (0, 50)! Notes: For linear utility function (perfect substitutes): ! If the indifference curves are steeper than the budget line ( MUx /MUy > Px /P y) or (MUx /Px > MUy/P y), the optimum is to consume only the good on the x-axis: (x * ,y*) = (1/Px ,0).! If the indifference curves are flatter than the budget line ( MUx /MUy < Px /P y) or (MUx /Px < MUy/P y), the optimum is to consume only the good on the y-axis: (x * ,y*) = (0,1/ P y).! If the indifference curves and the budget line have the same slope ( MUx /MUy = Px /P y) or (MUx /Px = MUy/P y), any combination on the budget line is optimum.!

Exercise 3.16! Julio receives utility from consuming food (F) and clothing (C) as given by the utility function U(F,C)=FC. In addition, the price of food is $2 per unit, the price of clothing is $10 per unit, and Julios weekly income is $50.! a) What is Julio’s marginal rate of substitution of food for clothing when utility is maximized?! U=FC are smooth convex indifference curves.! At optimal choice, the slope of the budget line and indifference curves are the same. The marginal rate of substitution, which is the slope of the indifference curve will be the same as the slope of the budget line, which is the price ratio.! Therefore, at the optimal choice we use the price ratio formula; MRSfc = Pf/Pc ! MRS(2)(10) = 2/10= 0.2! b) Suppose instead that Julio is consuming a bundle with more food and less clothing than his utility maximizing bundle. Would his MRSfc be greater or lower than answer in part a?! Marginal rate of substitution (MRSfc) theoretically asks; how many units of C to trade for/gain one more unit of F. This can be calculated as the ratio between two marginal utilities; MRSfc=MUf/ MUc! Marginal utilities are diminishing;! - If consumption of F increases, MUf decreases! - If consumption of C decreases, MUc increases! ! In both cases, the ratio MUf/MUc decreases ! Hence, MRSfc will be lower in (b) than in (a). ! c) Find the optimal bundle for Julio! • When U(F,C)=FC, this is a special case which means that the marginal rate of substitution (MRS)=C/F! • So at the optimum it must be C/F=2/10!

OR • Can also find this with the equal marginal principle; MUf/Pf = MUc/Pc! • MUf is the derivative of the utility function divided by the price of food ! • MUc is the derivative of the utility function divided by the price of clothes!

• The optimal bundle is on the budget line; 2F+10C=50 !

d) 10 years ago the price of food was $3 per unit, the price of clothing was $6 per unit. How did the cost of his life change since then according to Paasche index?! The Paasche Index takes the current bundle and calculates how much it would’ve cost 10 years ago, focuses on the current bundle. ! • • • • •

The current bundle is (C,F) = (2.5, 12.5) The current cost = $50! 10 years ago this bundle would’ve cost 6*2.5 + 3*12.5 = $52.5! 10 years ago, Julio would’ve had to spend more, it became cheaper.! Paasche index = 100 * current cost of current bundle / base cost of current bundle! Paasche index = 100 * 50/52.5 = 95.24!

Paasche Index Rules:! • If the index would be 100, the cost of living would not have changed! • If the index would be less than 100, the cost of living would be cheaper! • If the index would be more than 100, the cost of living would be more expensive than however many years ago. ! Exercise 3.17! The utility that Meredith receives by consuming food F and clothing C is given by U(F, C) = FC. Suppose that Meredith’s income in 1990s is $1200 and that the prices of food and clothing are $1 per unit for each. By 2000, however, the price of food has increased to $2 and the price of clothing to $3. Let 100 represent the cost of living index for 1990. Calculate the ideal and the Laspeyres cost-of-living index for Meredith for 2000. (HINT: Meredith will spend equal amounts on food and clothing with these preferences.)! In...

Pf

Pc

Extra

1990 $1

$1

I = $1200

2000 $2

$3

C + F = 1200

Cost of living index in 1990 is 100! Calculate:! A) The ideal cost of living index! B) The Laspeyres cost of living !

(a) The ideal cost of living ! Ideally, Meredith should be as well off in 2000 as she was in 1990 —> the same level of utility/ satisfaction!! Step 1: FInd her optimum (F, C) combination and utility in 1990 using:!

Step 2: Find het optimum (F,C) combination in 2000 given the utility level in step 1.! !

Step 3: Find her expenditure (E) on this new combination of F & C at 2000 prices!

Step 4: Calculate the cost of achieving U = 360,000 with 2000 prices relative to the cost of achieving that same level of utility with 1990 prices.!

(b) The Laspeyres cost of living index! Laspeyres: Let Meredith afford the optimum (F,C) combination of 1990 in 2000 as well.! Step 1: The total cost in 1990 is given: $1200! Step 2: With a budget of $1200, find the optimum (F, C) combination in 1990.! We already know this from (a) above: F* = 600 and C* = 600! Step 3: Calculate the cost of acquiring F = C = 600 with the 2000 prices.! $ E = (2*600) + (3*600) => $3000! Step 4: Calculate the cost of acquiring F = C = 600 with the 2000 prices relative to the cost of acquiring that came combination with 1990 prices.!

Note: The Laspeyres cost of living index overstates inflation relative to the ideal cost of living index.!

Chapter 4 Exercise 4.4 (a & b)! (a) Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate priceconsumption curve (for a variable price of orange juice) and income consumption curve. ! PCC: trace optimum points that result from changes in price of one good only (here, orange juice).! When they are perfect substitutes, the indifference curves will be linear (straight lines/constant slope lines).! Note: if the budget line and indifference curve coincide (are the same), any point on that line is an equilibrium ! !

Income Consumption Curve (ICC): trace optimum points that result from changes in income (price unchanged). Assume that apple juice and orange juice are not only perfect substitutes, but oneto-one perfect substitutes. !

Three Possible cases: 1.Orange Juice is cheaper (Po < Pa)! 2.Apple Juice is cheaper (Pa < Po)! 3.Orange juice and Apple Juice are the same price (Po = Pa)!

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(b) Left shoes and right shoes are perfect complements. Draw the appropriate price-consumption and income-consumption curves.! I) Price-consumption curve (PCC): only one price change.! Perfect complements are L-shaped indifference curves. !

II) Income consumption curve (ICC): income changes, price remain unchanged. !

Exercise 4.12! You run a small business and would like to predict what will happen to the quantity demanded for your product if you raise your price. While you do not know the exact demand curve for your product, you do know that in the first year you charged $45 and sold 1200 units and that in the second year you charged $30 and sold 1800 units.! (a) If you plan to raise your price by 10%, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms?! (b) If you raise your price by 10%, will revenue increase or decrease?! Given

Price ($)

Year 1

$45

1200

Year 2

$30

1800

!

Quantity (units)

(a) If you plan to raise your price by 10%, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms?! Using arc elasticity (particularly for large changes)!

With unit elastic demand of -1 there is a 10% increase in price, leads to 10% decrease in quantity demanded. ! (b) If you raise your price by 10%, will revenue increase or decrease?! Elasticity = -1, there is a percentage increase in price which means there is a percentage decrease in quantity. ! Revenue = Price x Quantity ! Revenue = Price (increase) x Quantity (decrease) —> they balance/ cancel out! Thus, revenue remains unchanged!! Exercise A4-4 (Appendix)! Sharon has the following utility function: U(X,Y) = √x +√y, where X is her consumption of candy bars, with price Px = $1 and Y is her consumption of espressos, with price Py = $3.! (a) Derive Sharon’s demand for candy bars and espresso! Maximize; U(X,Y) = √x +√y subject to the constraint PxX+PyY=I!

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(b) Assume that her income I = $100. How many candy bars and how many espressos will Sharon consume?! (c) What is the marginal utility of income?!

Chapter 19 Exercise 19.4! Suppose there are two types of e-book consumers: 100 “standard” consumers with demand Q = 20 - P and 100 “rule of thumb” consumers who buy 10 e-books only if the price is less than $10. (Their demand curve is given by Q = 10 if P < 10 & Q = 0 if P >= 10). Draw the resulting total demand curve for e-books. How was the “rule of thumb” behavior affected the elasticity of demand for e-books?!

How has the “rule of thumb” behavior affected the elasticity of demand for e-books?...