Define & Explain
Marginal rate of substitution
The MRS shows how much of one good a consumer is willing to give up to gain more of another good while keeping satisfaction constant.
It reflects the consumer’s trade-off and equals the slope of the indifference curve.
Explain the price discrimination at Costco and at Wendy's, and other other form of price discrimination.
Costco targets low price to their members, using membership fees to lock people into purchasing.
Wendy’s faced backlash for testing time-based menu pricing, with increased prices at rush hours
If I have a revenue equations R(q) = Aq^2 + Bq + C.... What must be true about A / B / C ? Why?
A must be negative, because the demand curve P(q) must have a downward slope
What is the marginal rate of substitution of a Utility function U(x1, x2) = (x1^0.4)(x2^0.7)? Why?
MRS12 = 4x2 / 7 x1 ... This is the slope of the indifference curve for these utilities, along which you're willing to give up fewer units of x2 for x1 and so on...
Define & Explain - Demand curve
A demand curve shows the relationship between the price of a good and the quantity consumers are willing to buy.
It usually slopes downward, meaning lower prices lead to higher quantities demanded
Indifference Curve
An indifference curve shows all combinations of two goods that give a consumer the same level of satisfaction.
Each curve represents a constant utility level, and higher curves indicate greater satisfaction.
Connect global birthrates with indifference curves -- What does the optimization here look like?
Income effect -- When the price per quality goes down (quality goes up), parents have MORE kids at similar quality
You can think about it as a good 1 being the # of children; and good 2 being the quality of children's lives. Government programs to support higher quality of children's lives look to entice possible parents to have more kids thought in the income effect. [Income effect -- When the price per quality goes down (quality goes up), parents have MORE kids at similar quality; Substitution effect -- When the price per quality goes down (quality goes up), parents have LESS kids at highest possible quality]
If P = 2000 - 0.1Q, what is the maximum possible revenue?
Max revenue is when Q = 10,000 and R = 10,000,000
If a product has a price elasticity of -1.6; an initial price of $50 and the initial quantity demanded was 20 units, what will happen if the firm cuts the price by 10%? Why would we expect this to happen?
Quantity increases by 16%, to 23.2 units. this is because the good is ELASTIC so price sensitive
Define & Explain -- Income Elasticity
Income elasticity measures how responsive the quantity demanded of a good is to a change in consumer income.
It shows whether a good is normal (Ey > 0) or inferior (Ey < 0), and how strongly demand changes as income rises or falls.
Substitute
A substitute is a good that can replace another in consumption.
When the price of one good rises, the demand for its substitute increases.
Explain for getting the correct number of taxi's in a city is an optimization problem
Too few cars cause long waits; too many create congestion and lower wages. If you can understand the relationships between Waits (W) and taxis (Q); as well as, Congestion (C) and taxis (Q) -- you can think through the interplay between W(Q) and C(Q)
For a company with R(Q) = -10Q^2+10Q; C(Q) = 5Q, at what amount Q can they make the most money? Why is that the spot?
Looking for Marginal Profit = 0; Q* = 0.25; Profit = 0.625
If U(x1,x2) = (x1^0.7)(x2^0.9) and and you have a budget of $1000, with x1 costing $50 and x2 costing $20, what is the optimal bundle? Why is this the optimal bundle?
x1 =8.75; x2 = 28.125; At this ratio, the consumer will maximize the potential utility within their given budget
Define & Explain - Quadratic Formula
What is (-b +/- sqrt( b^2 -4ac))/(2a)
A good is inelastic when demand changes little in response to price changes.
This means consumers continue buying nearly the same amount even if the price increases or decreases.
Explain how the price elasticity of Electric Vehicles as it relates to government subsidies
Demand for EVs is highly price-elastic, so a subsidy should make a strong difference in encouraging adoption.
If Qb has a demand of Qb = 100 - 0.5Pb; and a cost of Cb = 50Qb. And Qk has a demand of Qk = 600 - 5Pk and a cost of Ck=80Qk. How would suggest we maximize profit against the two goods (b) and (k)? Why? Solve it.
Maximize profit for both and add! Qb*= 37.5; Qk*=100; Total profit = 4,812.5
If a good has a cross-price elasticity of -0.8, explain what this means. What would happen to the original good if the cross-price good had a price increase of 30%?
The other goods demand will drop by 24%
Define and Explain -- Optimal mark-up
The optimal mark-up is the price increase over cost that maximizes a firm’s profit. Only for elastic demands.
Income effect
The income effect shows how a change in income (or purchasing power) affects the quantity of a good demanded.
When income rises, consumers usually buy more normal goods and fewer inferior goods.
Explain the price & income elasticity of alcohol and the policy implications
Alcohol is price inelastic (-0.29 to -0.54) so when prices rise, consumption doesn't fall by much. Therefore, taxes won't change demand much.
Alcohol is a normal good, so as incomes rise so does consumption. Therefore, economic growth can lead to more consumption.
Government might consider more targeted interventions to reduce alcohol overconsumption.
(SEE 400 FIRST) If Qb has a demand of Qb = 100 - 0.5Pb; and a cost of Cb = 50Qb. And Qk has a demand of Qk = 600 - 5Pk and a cost of Ck=80Qk. BUT! Say the total of Qb and Qk can only be 200 -- What does this change? What if it can only be 100?
200 is not a constraint because the max profit for both individually summed together is below that.
For 100, Qb =~34; Qk = ~66 for a total profit of $4,556.82
A cereal company estimated the following function for the demand of its cereal:=3.0−2.0+1.5+0.8−3.0+1.0Where Qxis the sales of the cereal in millions of boxes, Pxis the price of the cereal in dollars, I is national income in trillions of dollars, Pyis the price of the most similar competitor cereal, PMis the price of milk, and A is the advertising expenditures of the company, in hundreds of thousands of dollars.This year, Px= $2, I = $4, Py= $2.50, PM= $1, and A = $2. If PM increases by 30% how will this change sales?
Q initial is 9.6 million boxes of cereal; We would expected 0.9million fewer boxes with the milk spike (COMPLEMENTS) so we'd see a -9.38% drop in sales.
Define & Explain - Shadow Price
A shadow price is the implicit or estimated value of a resource that doesn’t have a market price, such as time or clean air.
In optimization problems, it shows how much the objective (like profit or utility) would increase if one more unit of a constrained resource were available.