BECO Exam 2

Special Types of Indifference Curves

Perfect Compliments - Point A: 2 right and 2 left shoes. Utility level of U2 - Point B: 3 right and 2 left does not increase utility. Still U2 - goods must be consumed together at the same rates to increase utility

Special Types of Indifference Curves

Perfect substitutes - in the case of perfect substitutes, the IC will be straight - constant MRS

Production Function

Q= F(K,L)

MRS Example

Slope from A to B: Rise/Run= -2/1= 2. This person is willing to give up 2 wings for one more beer and be at the same level of utility

Ex 3: Suppose we estimated demand to be Q= 1,000- 100P. What is Eqp if current price is $4?

Solve for Q when P=4- 1,000- 100(4)= 600 -100 x 4/600= 2/3

Income elasticity

The % change in q as a result of a % change in income Formula: change in Q/ change in I x income/quantity Values: EqI > 0= Normal good if positive. Increase income, increase purchasing EqI > 1= Luxury good EqI < 0= Inferior good answer will be negative. increase income, decrease purchasing

Cross-Price elasticity

The % change in q as a result of a % change in the price of a related product Formula: Change in Qx/Change in Py x Py/Qx Values: Eqp > 0= Substitutes, Qx & Py move in same direction Eqp <0= Compliments, Qx & Py move opposite directions

Supply elasticity

The % change in quantity supplied as a result in a % change in price Responsiveness of Qs (producers) to price changes Values: Es >1= Elastic 0<Es<1= Inelastic Es=1 = unit elastic

On a 250-acre farm, a farmer is able to produce 4,500 bushels of wheat when he hires 2 workers. He is able to produce 6,300 bushels of wheat when he hires 3 workers. Which of the following possibilities is consistent with the property of diminishing marginal product?

The farmer is able to produce 7,560 bushels of wheat when he hires 4 workers.

Average Variable cost

VC/Q

Percentage Change

% change= New-old/old

Production technology

- Characterizes how the firm turns input into output - For simplicity, we will consider a 2-input case: Labor (L) and Capital (C). Firms need to understand the relationships and properties of their production tech. -How much output can be produced with given level of inputs - Associated cost of producing that level of output - How production changes as scale of operations changes

Returns to scale in LR

- How does productivity change as the scale of operation changes? - Think... if I double my inputs, what happens to my outputs?

Production in the LR

- In the Long run, all costs are variable - can easily substitute between K & L - can still find MPl, MPk, etc

Diminishing MRS

- MRS can vary along the indifference curve bc the consumption of one good can be pushed too far. - In wings/beer example: MRS from A to B: 2 MRS from C to D: 1/2

Costs in the SR

- Recall that in the SR, some factors of production are fixed, we assume K TC= FC+VC

Marginal rate of substitution

- The number of units of Y that must be sacrificed for a unit of X - Indifference curves describe tradeoffs and the slope captures this tradeoff.

Productivity importance

- Total Product (TP): amount of total output that can be produced using a given level of inputs - Average Product or Labor (APl): amount of output that each unit of labor produces, on average, given the fixed amount of K

Average Cost

- a common measure of "cost per unit" TC/Q

Sunk Cost

- a cost already committed and cannot be recovered - when making decisions, you should ignore sunk cost

Marginal Product of Labor

- additional product of output that can be produced if one more unit of labor is used - MPL= Change in Q/ Change in L

Short run v. Long run

- another important factor in production decisions is the time frame - firms may have different options for different time horizons - firms face more constraints in the short run - we need to differentiate between 2 time horizon categories regarding production

Production in SR

- assume K is fixed - firms only option for changing production is L - ex: retail firms, service businesses

TT= TR-TC

- cheapest way - in order for firms to maximize profits, they must minimize costs

Law of Diniminshing Returns (diminishing marginal product)

- holding all other factors constant, an increase in input will eventually lead to smaller increase in output - EX: Too many cooks in the kitchen

Long Run costs

- in the LR, a firm has the flexibility using diff combinations of inputs - in the 2 inputs case, we want to choose the level of L & K that produce a given level of Q at the best cost

Economies of Scope

- refers to the cost properties when firms produce multiple prod - often, there can be cost saving efficiencies if firms produce multiple products

Economies of scale

- the property of how firms cost change as Q increase - Econ of scale: LR ATC is decrease as Q increase - diseconomies of scale: LR ATC is increasing as Q decreases - min efficient scale: level of output when the firms LR ATC is the lowest

Why are production decisions important

- they can impact efficiency with which output is provided - impact cost of production - firms profit - production decisions by firms drive the supply side of the market

LR Average total costs

- to get the LR etc, simply trace out the cost of the cost min bundle of L & K for each level of Q - LR ATC is always less than or equal to SR ATC bc firms have greater flexibility in LR, and can choose which SR curve it wants

Budget Constraint Example: Px=5, Py=10, I=8

-Budget line function: 5x+10y=80 - Slope?: -.5

Consumer equilibrium

-the objective of the consumer is to choose the consumption bundle w/ the highest utility while still being within budget - slope of indifference curve=slope of budget line - A: not spending all income - B: reallocating gets higher utility - C: would be great, can't afford - D: this is consumer equilibrium KEY: utility max occurs at the point of the tangency between the indifference curve & budget line. MRS=Px/Py

If a 16 percent increase in price for a good results in a 7 percent decrease in quantity demanded, the price elasticity of demand is (please use the Algebraic Point formula and insert your solution as a positive number)

.44

Which of the following could be the price elasticity of demand for a good for which a decrease in price would decrease total revenue?

.8

Budget Line shifts

1. Change in income - will shift entire budget line - more income = purchase more of both goods = shift outwards - less income = purchase less = shifts inwards - Slope does not change

If the cross-price elasticity between goods A and B is negative, we know the goods are

complements

Assume that the price elasticity of demand is 2 for a certain firm's product. If the firm raises price, the firm's managers can expect total revenue to

decrease

If Farmer Brown plants no seeds on his farm, he gets no harvest. If he plants 1 bag of seeds, he gets 5 bushels of wheat. If he plants 2 bags, he gets 9 bushels. If he plants 3 bags, he gets 12 bushels. A bag of seeds costs $120, and seeds are his only cost.

diminishing marginal product

If apples have an own price elasticity of 1.2 we know the demand is

elastic

Price (Dollars per unit) Quantity Demanded (Units) 200 0 160 30 120 60 80 90 40 120 0 150 Refer to the above table. If the price falls from $160 to $120, the price elasticity of demand is (please use the Midpoint formula)

elastic

efer to the above figure. Between point A and point B on the graph, demand is (please use the Midpoint formula)

elastic, but not perfectly elastic

The quantity consumed of a good is relatively unresponsive to changes in price whenever demand is

inelastic

When the price of candy bars is $1.20, the quantity demanded is 490 per day. When the price falls to $1.00, the quantity demanded increases to 500. Given this information, we know that the demand for candy bars is (please use the Midpoint formula)

inelastic

When large changes in price lead to no changes in quantity demanded, demand is perfectly

inelastic, and the demand curve will be vertical

An income elasticity less than zero tells us that the good is

inferior

Goods with many close substitutes tend to have

more elastic demands

A consumer consumes two normal goods, popcorn and Pepsi. The price of Pepsi rises. The substitution effect, by itself, suggets that the consumer will consume

more popcorn and less Pepsi

Production

process of turning inputs to outputs. - can be final goods, intermediate goods, or services - there are usually multiple ways to produce a good/service (ex. hand-made vs automation)

Lemonade, a good with many close substitutes, should have an own price elasticity that is

relatively elastic

Budget Constraint

the budget constraint restricts consumer behavior by forcing the consumers to select a bundle of goods that is affordable Budget line= Px(X)+Py(Y)= Income

Income & Substitution effects

the impact of a change in the price of a good on the quantities purchase can be composed into 2 effects: Income effect and substitution effect

Price Elasticity of demand

the percentage change in the quantity demanded of a good in response to a one percent change in its price

Utility

the pleasure or satisfaction that ppl get from their economic activity a measure of happiness

Midpoint (arc) Formula

change in Q/ 1/2(Q1+Q2) / change in P/ 1/2 (P1+P2)

Factors that affect Eqp

1. Closeness of substitutes - more sub. more elastic (easer to with if P increases) - EX: not many subs for insulin, so it is inelastic 2. Proportion of income - higher proportion of income, more elastic - EX demand is very inelastic for sugar or flour, but relatively more elastic for cars 3. Time Horizon - longer time horizon, the more elastic - EX: gas is virtually perfectly inelastic in a weeks time, but is much more elastic over a year 4. Ease of storage - easier it is to store, the more elastic -EX: paper towels are more elastic than services 5. Type of good - necessity v. luxury -EX: lux goods typically have more elastic demand

Assumptions about preferences

1. Completeness- An individual is able to state if A>B, A<B, or A=B. 2. Transitivity- If A>B & B>C, then A>C 3. More is better- a person always prefers more of a good to less

Indifference curve properties

1. Higher indifference curves are preferred to lower ones, if U1=10 and U2=20, U2 would be preferred. 2. Indifference curves slope downward (negative) - describes tradeoffs - if quantity of one good increases, the quantity of the other must decrease for the consumer to be equally happy 3. Cannot Intersect - For example: U1 has points A & B, so indifferent. U2 has points A & C, so indifferent. So if A & B and A & C are indifferent, B should be however it has more of both X & Y. 4. Bowed inward - bc of diminishing marginal rate of substitution

EX: lets say one is interested in Pepsi & pizza and the price of Pepsi falls.

1. Income effect - "now that Pepsi is cheaper my income has greater purchasing power. I am, in effect, richer than I was before, I can buy both more Pepsi and pizza" 2. Substitution effect - "now that the price of Pepsi has fallen, I get more liters of Pepsi for every pizza that I give up. bc pizza is relatively more expensive, I should buy less pizza and more pizza."

Cost min in the LR

1. experimentation (impractical and costly) 2. use info about productivity of inputs and costs - cost min requires that the relative productivity is equal at the given amount we are using - Last $ rule: pick the combo of inputs such that the last dollar spent on each input generates the same marg. prod - Mpl/w=MPk/r

Minimizing cost will depend on 2 main measures

1. productivity of each input 2. cost of each input

Refer to the above figure. Moving from point A to point B, price elasticity of demand is equal to (please use the Midpoint formula and insert your solution as a positive number) A- P=7, Q=12 B- P=5, Q=20

1.5

Suppose a certain firm is able to produce 125 units of output per day when 19 workers are hired. The firm is able to produce 137 units of output per day when 20 workers are hired, holding other inputs fixed. The marginal product of the 20th worker is

12

Refer to Figure 1. If the consumer's income is $221, then what is the price of a CD? (Please insert your solution without a dollar sign)

13

Budget Line shifts

2. Change in price - will change the slope

Price (Dollars per unit) Quantity Demanded (Units) 200 0 160 30 120 60 80 90 40 120 0 150 Refer to the above table. If the price falls from $160 to $120, the price elasticity of demand is (please use the Midpoint formula and insert your solution as a positive number)

2.33

Suppose: Mpl=200 W+$100 MPk=1,000 r=$1,000

200/100= for every dollar you spend, 2 units of output 1,000/1,000= 1 since MPL/W > MPK/R, use more labor

If the price elasticity of demand for a good is 5, then a 10 percent increase in price results in a (please use the Algebraic Point formula)

50.00 percent decrease in the quantity demanded

Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of output. Assume two points on the firm's production function are (L = 12, Q = 122) and (L = 13, Q = 130). Then the marginal product of the 13th worker is

8

Eqp ex 2: Suppose that Eqp= -.5 and your firm is contemplating a price increase of 10%. How much will sales drop by?

= .5/10 = .05, sales will drop by 5%

Eqp example: Find Eqp using midpoint, interpret Eqp, elastic or inelastic demand? From P=2 and Q= 25 To P=3 and Q=15

= 10/ .5(25+15) / -1/ .5(2+3)= -.5/.4= 1.25 a 1% increase in price causes a 1.25 decrease in demand elastic because greater than 1

Eq,p example 1: Suppose sales rise by 20% when price was dropped by 5%. Eqp?

= 20/-5 = -4 or 4

Average product of labor

APL=Q/L

Ex 4: Assume starting p=4 and q= 25, Eqp?

Algebraic Point: 20-25/25 / 5-4/4= -.8 or .8 Midpoint: 20-25/ .5(20+25) / 5-4/ .5(5+4)= -.222/.222= 1

Ex 5: Assume starting P=5 and q=20

Algebraic Point: 25-20/20 / 4-5/5= -5/4 or -1.25 or 1.25 Midpoint: 25-20/ .5(25+20) / 4-5/ .5(4+5)= 1

Long run

All inputs are variable (this distinction is about how constrained the firm is)

Short Run

At least input is fixed (usually)

Constant return to scale

Doubling all inputs exactly doubles output - production doesn't always exhibit CRS

Decreasing returns to scale

Doubling all inputs less than doubles outputs - coordination problem - quality control - managerial problems

Increasing returns to scale

Doubling all inputs more than doubles outputs - Specialization and learning-by-doing - bigger, faster machines

Algebraic point formula

Eq,p= -b x p/q (-b is slope of demand curve) - local measure - will always be negative - how responsive is Qd to changes in price along this portion of the demand curve - express as absolute value - problem with this is it gives different Eqp answers over the same range depending on starting point - only use as a basis for the midpoint formula

Example

Example

Average Fixed cost

FC/Q

Indifference Curve

a curve that shows all the combinations of goods that provide the same level of utility shows bundles a consumer is indifferent between all points along the same line, a person would be indifferent between

Elasticity

a measure of the percentage change in one variable brought about by a 1% change in some other variable "responsiveness"

Marginal Cost

additional cost of producing one more unit of output MC= Change in TC/Change in Q

If the price elasticity of demand for steak is 0.4, an increase in price will lead to

an increase in total revenue