ECO 100

Microeconomics -- Midterm Prep

How to find equilibrium?

Set $Q^{D}\left(P\right)=Q^{S}\left(P\right)$, solve for equilibrium price $P$

Plug back into either supply or demand for the quantity $Q$

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Example:

$Q^{D}\left(P\right)=100-10P$ and $Q^{S}\left(P\right)=15P$

Setting equal gives: $P=4$

Plug back into supply or demand to get quantity 60.

Supply shifts right/increases when…?

Supply shifts to the right when suppliers are more willing to produce

• input costs decrease

• technology improves

Supply shifts left/decreases when…?

Supply shifts to the left when suppliers are less willing to produce

• input costs increase

• technology is damaged/worsened

Demand shifts right/increases when…?

Demand will shift right if consumers are more eager to buy

• complement good gets cheaper

• consumers anticipate/expect high/higher future value

• a substitute good gets more expensive

Demand shifts left/decreases when…?

Demand will shift to the left when consumers are less eager or willing to buy

• complement good gets more expensive

• future value anticipated to be low

• a substitute good becomes more affordable

Equilibrium price RISES when?

Equilibrium price FALLS when?

Equilibrium price RISES when demand shifts right or supply shifts left

Equilibrium price FALLS when demand shifts left or supply shifts right

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A demand shift moves price and quantity the same direction

A supply shift moves them in opposite directions

• e.g., if supply shifts right, then equilibrium price falls and quantity rises

What is a price floor?

A price floor is a minimum price

e.g., minimum wage

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• a price floor is binding if it is too high

  • i.e., above the equilibrium price

• causes surpluses, as supply exceeds demand if the price is too high

• the short side of the market (here, demand) determines quantity actually traded

• suppliers who get the high price BENEFIT, consumers who pay this do NOT, sellers who previously managed to sell (but now cannot) are HARMED

  • e.g., workers who previously had their jobs, “sold their labor,” but now are unemployed)

When is a price floor BINDING? And what is the impact of a binding price floor?

• a price floor is binding if it is too high

  • i.e., above the equilibrium price

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binding price floors cause surpluses

BUT, sometimes, a regulating agency will buy up the surplus which results in:

• higher prices for suppliers (here, farmers): good

• higher prices for consumers: bad

• high government costs: bad

Minimum wage is an example of what kind of price regulation?

Bonus: Draw a graph which illustrates the impact of minimum wage on the supply and demand graph.

Multiple Choice: To help poor workers, the government imposes a minimum wage. Assuming that this is binding, our equilibrium supply/demand model predicts: wages and unemployment

A. rise, rises

B. rise, falls

C. fall, rises

D. fall, falls

A price floor.

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**see the graph in the photo for the correct illustration

Your axis should be labeled:

Y-axis — Hourly Wage (price)

X-axis — Number of Workers (quantity)

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Multiple Choice: To help poor workers, the government imposes a minimum wage. Assuming that this is binding, our equilibrium supply/demand model predicts: wages and unemployment

A. rise, rises

B. rise, falls

C. fall, rises

D. fall, falls

What is a PRICE CEILING?

A price ceiling is a maximum allowed price.

e.g., rent control

When is a price ceiling BINDING? What does this cause? What impact does this have?

Bonus: Draw a graph illustrating a binding price ceiling

A price ceiling (maximum allowed price) is binding when it is below the equilibrium price.

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A price ceiling causes shortages which may result in:

• long lines

• reduction in quality of goods sold

• black market sales

• lotteries

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Shortages are created because demand exceeds supply when the price is too low

The short side of the market, supply here, determines quantity actually traded

What is elasticity?

Write or recite the formula from memory.

Elasticity measures how responsive/sensitive quantity demanded or supplied is, in one of the things that influences it

Formula:

Price Elasticity $=\frac{\%\Delta Q^{D}}{\%\Delta P}=\frac{\frac{\Delta Q}{Q}}{\frac{\Delta P}{P}}=\frac{P}{Q}\cdot\frac{1}{\frac{\Delta P}{\Delta Q}}$

Define price elasticity of demand

Write or recite the formula from memory.

How responsive demand quantity is to price.

For demand, the slope is negative.

Formula:

$$\epsilon_{P}^{D}=\left|\frac{\%\Delta Q^{D}}{\%\Delta P}^{}\right|=\frac{P}{Q^{D}}\cdot\frac{1}{\left|slope\right|}$$

Price elasticity of demand gets higher as we move to the top left of demand.

• with higher $P$ and lower $Q$

• it also gets higher as |slope| falls, i.e. as demand gets flatter

Define inelastic demand

Inelastic demand means that if price falls $→$ quantity barely rises $→$ expenditures fall

Inelastic demand = fairly insensitive

$\left|\epsilon_{p}\right|<1$ , meaning “quantity changes by a smaller proportion than price”

Define elastic demand

Elastic demand means that if price falls $→$ expenditures are directly reduced $→$quantity rises by more than enough to compensate $→$ meaning overall, expenditures rise

Elastic = highly sensitive

$\left|\epsilon_{p}\right|>\>1$ meaning “quantity changes by a larger proportion than price”

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more elastic $\leftrightarrow$ less eager to trade

less elastic $\leftrightarrow$ very eager to trade

Calculating a SHORTAGE
Write the formula.

$$Q^{D}\left(P\right)-Q^{S}\left(P\right)$$

calculated at ceiling price!

Calculating a SURPLUS

Write the formula.

$$Q^{S}\left(P\right)-Q^{D}\left(P_{}\right)^{}$$

calculated at the floor price!

Inelastic

Price elasticity of demand ($\left|\epsilon_{P}\right|$ ) is inelastic when it is?

$$\left|\epsilon_{P}\right|<1$$

Inelastic

Elastic

Price elasticity of demand ($\left|\epsilon_{P}\right|$ ) is elastic when it is?

$$\left|\epsilon_{P}\right|>1$$

Elastic

Unit Elastic

Price elasticity of demand ($\left|\epsilon_{P}\right|$ ) is unit elastic when it is?

$\left|\epsilon_{P}\right|=1$

Unit elastic means a percentage change in price causes an equally proportional percentage change in the quantity demanded or supplied

Perfectly Inelastic (vertical)

Price elasticity of demand ($\left|\epsilon_{P}\right|$ ) is perfectly INELASTIC when it is?

Vertical

$\epsilon_{P}=0$

Perfectly Elastic (horizontal)

Price elasticity of demand ($\left|\epsilon_{P}\right|$ ) is perfectly ELASTIC when it is?

Horizontal

$$\left|\epsilon_{P}\right|=\infty$$

Formula for Expenditure

Bonus: What happens to expenditures in elastic vs. demand systems in response to changes in price?

expenditure $=P\cdot Q^{D}\left(P\right)$

Elastic: price falls $→$ expenditure rises

Inelastic: price falls $→$ expenditure falls

What makes demand elastic?

Close substitutes and more time (long run). Necessities are inelastic. Supply is inelastic when quantity is hard to adjust (beachfront land). The elastic side is less eager to trade.

Marginal Benefit (MB)

Dollar valuation approach!

MB: Maximum willingness to pay

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Can be used to determine individual demand

Marginal Cost (MC)

The minimum you’d sell one more unit for.

MB curve = demand

MC curve = supply

Producer Surplus

For a standard straight-line supply curve forming a triangle:

• Producer Surplus = $\frac12\times Base\times Height$

• $Base=Equilibrium$ $Quantity (Q^*)$

• $Height=Equilibrium$ $Price\left(P^{\ast}\right)-Supply$$Intercept\left(P_{\min}\right)$

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Producer Surplus = $\frac12\times Q^{\ast}\times\left(P^{\ast}-P_{\min}\right)$

Formulas for $P^{C}$ and $P^S$ when consumers pay the tax directly

Bonus: what happens to demand when consumers pay directly?

$$P^{C}=P+t$$

$$P^{S}=P$$

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demand decreases by $t$

Formulas for $P^{C}$ and $P^S$ when suppliers pay the tax directly

Bonus: what happens to supply when suppliers pay directly?

$$P^C=P$$

$$P^S=P-t$$

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supply increases by $t$

Equilibrium with a tax

$$Q^{D}\left(P^{C}\right)=Q^{S}\left(P^{S}\right)$$

Per-unit subsidies wedge

$$P^C=P^S-s$$

Per-unit subsidies when consumers receive it

$$P^C=P-s$$

$$P^S=P$$

Demand shifts up by $s$.

Per-unit subsidies when suppliers receive it

$$P^{S}=P+s$$

$$P^{C}=P$$

Supply shifts down by $s$.

Cost, total surplus, and DWL in response to subsidies

cost $=sQ^*_1$

$TS=CS+PS-$cost

$$DWL=\frac12s(Q_1^{*}-Q^{*})$$

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CS and PS both rise, but the cost rises by more.

DWL = trades that happen but shouldn’t (MC > MB).

Draw a graph based on the following scenario, and answer the questions below (make sure they are visible on the graph too):

World price is less than domestic equilibrium, and the government institutes a tariff per unit.

World price $p^{world}=\$10$

Tariff per unit (imports only) =$10

1. What is the PS gain/loss?

2. What is the CS gain/loss?

3. Is there a DWL? If so, what is it?

4. What is the total revenue?

1. What is the PS gain/loss? PS gain = 300

2. What is the CS gain/loss? CS loss = -750

3. Is there a DWL? If so, what is it? Yes, DWL = 150

4. What is the total revenue? Revenue = 300

You might not need to calculate all of these number values depending on how complex the graph is but it would be safe to familiarize yourself with them to make sure that you can read them easily off of a graph/interpret the numbers.

Formula for budget constraint and line

$$p_1x_1+p_2x_2\le m$$

$$p_1x_1+p_2x_2=m$$

The budget line is the bundles that use up exactly all your money.

Marginal Rate of Substitution (MRS)

$MRS_{1,2}=\frac{MU_1}{MU_2}=$ |slope of indifference curve|

The rate you’re willing to give up good 2 for one more of good 1.

Formula for Optimal Bundle

$\frac{MU_1}{MU_2}=\frac{p_1}{p_2}$ $\&$ $p_1x_1+p_2x_2=m$

On the graph, the indifference curve just touches the budget line.

Bang per buck

$$\frac{MU_1}{p_1}=\frac{MU_2}{p_2}$$

Conditions (involving marginal utility) which are not optimal

$$\frac{MU_1}{MU_2}>\frac{p_1}{p_2}\lrArr\frac{MU_1}{p_1}>\frac{MU_2}{p_2}$$

If one good has a greater “bang-per-buck” than the other, then the bundle is not optimal.

Compare per dollar, not raw $MU$

What does the MRS look like at the optimum bundle?

$$MRS_{1,2}=\frac{p_1}{p_2}$$