Question 1

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

The price elasticity of demand (PED) is calculated using the formula: PED = (dQ/dP) * (P/Q), where dQ/dP is the derivative of the demand function with respect to price, P is the price, and Q is the quantity demanded. For the given demand function Q = 100 - 4P, dQ/dP = -4. At P = $10, Q = 100 - 4(10) = 60. Substituting these values into the PED formula gives: PED = (-4) * (10/60) = -40/60 = -2/3 = -0.67.

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 price elasticity of demand, which measures how sensitive consumers are to changes in price. The slope of the demand curve and excess demand are related concepts but do not directly refer to the percentage change in quantity demanded in response to a percentage change in price.

Question 3

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

The price elasticity of demand (PED) formula is (dQ/dP) * (P/Q). Given the inverse demand curve Q = 50 - 2p, when p = $3, Q = 50 - 2(3) = 44. The derivative of Q with respect to p (dQ/dP) is -2. Substituting these values into the PED formula gives -2 * (3/44), which matches option C.

Question 4

The local lemon market has the following supply and demand relationships: Q_D= 100 - 5p - p_o+ 2I Q_S= 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 p_o 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.

Accepted Answer

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Question 5

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: Q_S= 20r + 100p Q_D= 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)?

Accepted Answer

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Question 6

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

To find the price where demand has unitary elasticity, we need to find the price at which the absolute value of the elasticity of demand is equal to 1. The elasticity of demand for orange juice is given by:

E = (% change in quantity demanded)/(% change in price) = (dQ/Q)/(dp/p) = (dQ/dp)*(p/Q)

Taking the derivative of the demand function with respect to price, we get:

dQ/dp = -500

Plugging in the values we have:

E = (-500)*(p/Q)

Since the demand function is linear, we can substitute the price into the demand function to find the corresponding quantity demanded:

Q = 2000 - 500p

When p = $2, we get:

Q = 2000 - 500(2) = 1000

Now we can substitute these values into the elasticity formula:

E = (-500)*(2/1000) = -1

Since we want the absolute value of E to be 1, we can take the negative sign away:

E = 1

Therefore, the demand for orange juice has unitary elasticity at a price of $2 per gallon.

Question 7

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

Accepted Answer

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Question 8

The supply and demand for wheat are given by Q_S= 20 + 100p Q_D = 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.

Accepted Answer

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Question 9

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).

Accepted Answer

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Question 10

If the demand curve for a good always has unitary price elasticity,what does this imply about consumer behavior?

Accepted Answer

Unitary price elasticity means that a change in price leads to an equal percentage change in the quantity demanded. This suggests that consumers do not have a strong reaction to price changes and will continue to purchase a roughly constant amount of the good regardless of its price. Therefore, they will spend a constant total amount on the good, as stated in choice B.

Question 11

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

Accepted Answer

Unitary elasticity occurs when the percentage change in quantity demanded is equal to the percentage change in price. In this demand curve, when price is halved, quantity demanded doubles (for example, when price is $100, quantity demanded is 100, but when price is $50, quantity demanded is 200). This means that the percentage change in quantity demanded is always equal to the percentage change in price, resulting in unitary elasticity at all price points.

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

Accepted Answer

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 the responsiveness of quantity demanded to a change in price, and a high magnitude of the coefficient (in absolute terms) suggests a relatively elastic demand.

Question 13

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?

Accepted Answer

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Question 14

-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?

Accepted Answer

The answer of 
-The above figure shows the demand curve...

Question 15

The demand curve for Widgets is given by Q_D = 5800 - 200p + 30p_G where Q_D is the quantity of widgets demanded,y is the per capita income and p_G is the price of Gizmos.The supply of Widgets is given by: Q_S = 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.

Accepted Answer

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Question 16

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

Elasticity is calculated using the formula: % Change in Quantity Demanded / % Change in Price. 
At a price of $3, the quantity demanded can be calculated using the demand equation: 
Q = 2000 - 500(3) = 500 
At a price of $2, the quantity demanded can be calculated using the demand equation: 
Q = 2000 - 500(2) = 1000 
Using these values, we can calculate the percentage change in quantity demanded and percentage change in price:

% Change in Quantity Demanded = (1000-500)/1000 = 0.5

% Change in Price = (3-2)/3 = 0.33

Now, we can calculate elasticity:

Elasticity = % Change in Quantity Demanded / % Change in Price 
Elasticity = 0.5 / 0.33 
Elasticity ≈ 1.51

Since elasticity is greater than 1, demand is elastic. However, none of the answer choices match our calculation of elasticity. The closest answer is B, which has the correct sign (-3), but the absolute value is incorrect. We can calculate the absolute value of elasticity by taking the absolute value of the slope of the demand curve multiplied by the price-quantity ratio:

Absolute value of slope = |-500| = 500

Price-Quantity Ratio = (3+2)/2 / (500-1000)/2 = 1.5/-250 = -0.006

Absolute value of elasticity = 500 * 0.006 = 3

Therefore, the best choice is B.

Question 17

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

Accepted Answer

The answer of Using the supply and demand equations for...

Question 18

-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, the demand curve in the figure (not visible in this format) likely shows this characteristic, where a proportional change in price leads to an equal proportional change in quantity demanded.

Question 19

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?

Accepted Answer

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Question 20

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.

Accepted Answer

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Quiz 2: Supply and Demand