Question 1

Using the supply and demand equations for wheat above,determine how the equilibrium price and quantity vary with an increase in rainfall(r)holding other factors that influence supply and demand fixed.How do the equilibrium price and quantity change with an increase in income(I).Answer this comparative statics question using calculus.

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Question 2

The percentage change in the quantity demanded in response to a percentage change in the price is known as the

Accepted Answer

The percentage change in quantity demanded in response to a percentage change in price is known as the price elasticity of demand. This measures the responsiveness of consumers to changes in price and is calculated as the percentage change in quantity demanded divided by the percentage change in price. The slope of the demand curve is a measure of how steep or flat it is, while excess demand refers to a situation where the quantity demanded exceeds the quantity supplied at a given price. Therefore, only option C is the correct answer.

Question 3

-The above figure shows the demand curve for crude oil.The demand curve has unitary price elasticity when price equals

Accepted Answer

Unitary price elasticity occurs when the percentage change in quantity demanded is equal to the percentage change in price, resulting in an elasticity of 1. At a price of $10, given the linear nature of the demand curve depicted, this is the point where a proportional change in price would result in an equal proportional change in quantity demanded, indicating unitary elasticity.

Question 4

If the demand curve for comic books is expressed as Q = 10,000/p,then demand has a unitary elasticity

Accepted Answer

The demand curve Q = 10,000/p has an inverse relationship between price and quantity demanded. When the price decreases, the quantity demanded increases proportionally. As a result, the elasticity of demand is always unitary, or equal to -1. Regardless of the price, the percentage change in quantity is always equal and opposite to the percentage change in price, resulting in a unitary elasticity.

Question 5

-The above figure shows the demand curve for crude oil.If the market price is $10 a barrel,what is the price elasticity of demand?

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-The above figure shows the demand curve...

Question 6

Suppose the inverse demand curve for a good is expressed as Q = 50 - 2p.If the good currently sells for $3,then the price elasticity of demand is

Accepted Answer

To calculate the price elasticity of demand, we use the formula: E = (% change in quantity demanded)/(% change in price). 
Since the initial price is $3, and the inverse demand curve is Q = 50 - 2p, we can solve for quantity as Q = 50 - 2(3) = 44. 
If the price increases to $4, then the quantity demanded would be Q = 50 - 2(4) = 42. 
Using the formula, we get: E = ((42-44)/44)/((4-3)/3) = -2 * (3/44). 
Therefore, the answer is C.

Question 7

Using the supply and demand equations for wheat,solve for the equilibrium price and quantity as functions of I and r.

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Question 8

The local lemon market has the following supply and demand relationships:
QD = 100 - 5p - pₒ + 2I
QS = 4p
where p is the price of lemons (per pound),Q is the quantity of lemons in pounds,I is the average consumer income,and pₒ is the price per pound of oranges.Derive the equilibrium price and quantity of lemons as functions of the price of oranges and average consumer income.Use the calculus method of comparative statics to compute the effects of income and the price of oranges on the equilibrium price and quantity of lemons.

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Question 9

Use a supply-and-demand graph to predict what happens to sheet steel prices in the United States after quotas on Japanese and European sheet steel expire.

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Question 10

If the demand curve for orange juice is expressed as Q = 2000 - 500p,where Q is measured in gallons and p is measured in dollars,then at the price of $3,elasticity equals

Accepted Answer

To find the elasticity at a specific price, we use the formula:
E = (% change in quantity demanded) / (% change in price)

At a price of $3, the quantity demanded is:
Q = 2000 - 500(3) 
Q = 500

If the price increases from $3 to $4, the quantity demanded decreases to:
Q' = 2000 - 500(4) 
Q' = 0

The percentage change in quantity demanded is:
[(Q' - Q) / Q] x 100 
= [(0 - 500) / 500] x 100 
= -100%

The percentage change in price is:
[(4 - 3) / 3] x 100 
= 33.33%

Plugging these values into the elasticity formula, we get:
E = (-100%) / (33.33%)
E = -3

Therefore, the elasticity at a price of $3 is -3.

Question 11

Suppose that the supply and demand of wheat depend on the price of wheat (p),the amount of annual rainfall (r),and the level of disposable consumer income (I).The equations describing the supply and demand curves are given by:
QS = 20r + 100p
QD = 4000 - 100p + 10I
Sketch a graph of the supply and demand curves for wheat and show the effects of an increase in the quantity of rainfall.How does each curve shift (if at all)from the increase in rainfall? What does this shift do to the equilibrium price and quantity (increase/decrease)?

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Question 12

If the demand for orange juice is expressed as Q = 2000 - 500p,where Q is measured in gallons and p is measured in dollars,then at the price of $3,the demand curve

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The demand curve is elastic because the percentage change in quantity demanded is greater than the percentage change in price, indicated by the negative coefficient of price (-500) in the demand equation Q = 2000 - 500p. Elasticity measures responsiveness, and a high absolute value of the coefficient (in this case, 500) suggests a relatively elastic demand.

Question 13

The demand curve for Widgets is given by
QD = 5800 - 200p + 30pG
where QD is the quantity of widgets demanded,y is the per capital income and pG is the price of Gizmos.The supply of Widgets is given by:
QS = 250p - 1250
a.Solve for the equilibrium price and quantity of widgets in terms of the price of Gizmos.
b.Compute the comparative static derivatives for the changes in the equilibrium price and quantity of Widgets with respect to a change in the price of Gizmos.

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Question 14

What happens to the equilibrium price and quantity of coffee when there is a leftward shift of the supply curve for tea? Explain.

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Question 15

Suppose the demand function for a good is expressed as Q = 100 - 4p.If the good currently sells for $10,then the price elasticity of demand equals

Accepted Answer

Price elasticity of demand (PED) is calculated using the following formula:

PED = (% Change in Quantity Demanded)/(% Change in Price)

At the current price of $10, the quantity demanded is:

Q = 100 - 4p = 100 - 4(10) = 60

Now, if the price increases to $11, the quantity demanded will decrease to:

Q' = 100 - 4p' = 100 - 4(11) = 56

Thus, the % Change in Quantity Demanded is:

(% Change in Quantity Demanded) = (Q'-Q)/Q x 100% = (56-60)/60 x 100% = -6.67%

And the % Change in Price is:

(% Change in Price) = (p'-p)/p x 100% = (11-10)/10 x 100% = 10%

Now, using these values, we can calculate the price elasticity of demand as:

PED = (% Change in Quantity Demanded)/(% Change in Price) = (-6.67%)/(10%) = -0.67

Therefore, the correct answer is B.

Question 16

If an increase in income results in a rightward parallel shift of the demand curve,then at any given price,the price elasticity of demand will have

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Question 17

Using the supply and demand curve for wheat above,sketch the supply and demand curves demonstrating the effect of an increase in disposable consumer incomes.How does each curve shift (if at all)to the increase in income? What does the shift do to equilibrium price and quantity?

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Question 18

The supply and demand for wheat are given by
QS= 20 + 100p
QD = 4000 - 100p +10Y
Where Y is the average consumer income.
a.Compute the partial derivative of quantity demand with respect to changes in average consumer income.
b.Solve for the equilibrium price and quantity as functions of the consumer income.
c.Compute the derivatives of the equilibrium price and quantity with respect to income.

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Question 19

If the demand function for orange juice is expressed as Q = 2000 - 500p,where Q is quantity in gallons and p is price per gallon measured in dollars,then the demand for orange juice has a unitary elasticity when price equals

Accepted Answer

The formula for elasticity of demand is % change in quantity demanded / % change in price. When the elasticity is equal to 1, it means that the % change in quantity demanded is equal to the % change in price, resulting in no change in total revenue. At a price of $2, the quantity demanded will be Q=2000-500(2) = 1000 gallons. If the price increases to $3, the quantity demanded will decrease to Q=2000-500(3) = 500 gallons. This is a 50% decrease in quantity demanded ($500/1000) and a 50% increase in price ($1/$2), resulting in an elasticity of 1. Therefore, the correct answer is C.

Question 20

Suppose there is a linear downward-sloping demand curve and a linear upward-sloping supply curve for a good.The price of a substitute good increases and the price of an input to production also increases.Graph the original demand and supply curves,and the curves after the substitute good and input prices increase.How will the equilibrium price change after the substitute and input prices increase?

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Quiz 2: Supply and Demand