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(a) The demand curve is given by D = 8002p. The price rises from 100 to 150. What is the change in consumer surplus?

Unrelatedly, if the utility is U = x3y, then demands are x = (3I)/(4px) and y = (I)/(4py). Initially, I = 15000 and px = 80 and py = 100. Then the price of good y increases to 207.36.

(b) How much would you at most be willing to pay to avoid the price change (Calculate EV)?

(c) By how much would your income need to increase to be as well after the price change as before (Calculate CV)?

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Chika Ilonah
Chika IlonahLv10
29 Sep 2019

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Related questions

Suppose that a consumer's preferences over two goods, x and y, are represented by a Cobb-Douglas utility function:

U(x,y) = x1-i² yi²

a. Find the expenditure function of the consumer, and the compensated demand functions.

b. Suppose that i² = 1/4 and that initially a consumer is in equilibrium with px = 1,py = 1, I = 100. What are the demands for xand y.

c. What is the minimum increase in income necessary for the consumer to be as well offunder price px = 1, py = 2, as she/he was at prices px = 1, py = 1?

Explain why the percentage increase is smaller than the increase inthe CPI for the consumer that you derived in part c.

Use your knowledge about price-searching firms and two-part pricing to advise the company below. A company has a bar and is trying to decide on the cover charge (if any) and price for each drink. It has done a modest regression study in which it asked customers to classify themselves as light drinkers or heavy drinkers and to indicate the number of drinks they would typically consume during the evening. The estimate from the regression study is that a change in the price equal to $1 per drink causes light drinkers to change their consumption on average by 0.5 drinks per night. However, a change in the price of $1 causes heavy drinkers to change their consumption on average by 1.0 drinks per night. For both groups, a typical consumer will not consume anything once the price reaches $9 per drink. (They may instead go to another bar or not go to a bar at all.) Draw a demand curve for a typical light drinker and for a typical heavy drinker on the same diagram. Explain your diagram. Write equations for the curves in slope-intercept form.

If 300 people visit the bar on a typical evening, with 200 people being light drinkers and 100 people being heavy drinkers, draw an overall demand curve for all of the consumers combined. What is the slope and what is the intercept for this demand curve? Write an equation in slope-intercept form. If the marginal cost of making drinks (the alcohol, the bartender's labor, and the amortized cost of purchasing glasses and cleaning them repeatedly) is constant at $5 per drink, and if no cover charge is assessed, what is the best price to charge for drinks? How many drinks would be sold on a typical evening? What would your profits be? If you cut your price by $1 per drink and assess the maximum possible cover charge without causing a typical light drinker to refuse to enter the bar, would your profits improve? How high would the cover charge be? Calculate both the cover charge and your total profits. Would the new pricing increase profit?

Maybe the best price cut is not exactly $1. Write a profit equation. Profits equal to total revenue minus total cost. Total cost equals $5 times the number of drinks sold. Total revenue equals the price for drinks times the number of drinks sold, plus 300 people times the cover charge. The cover charge equals, for a light drinker, the triangle of consumer surplus above the price but below the demand curve for a light drinker. (The area of a triangle equals one half the base times the height.) You will take the derivative of the profit equation with respect to P or Q and set it equal to zero. For example, use the equation for the total demand curve and solve for Q in terms of P. Then in the profit equation substitute in an expression involving P in place of every Q that was in the original profit equation. Now you can take a derivative of profits with respect to P and set the derivative equal to zero. Eventually, you can solve for the exact best P, Q, and cover charge.

Review of the slope-intercept form: Y= a - bX; a = the intercept on the Y-axis and b = the absolute value of the slope (slope=(change in Y)/(change in X)) For a demand curve: P=a-b Q. The intercept on the vertical axis would indicate a price that is so high that the quantity demanded becomes zero. The slope is the ratio of a change in price divided by the change in quantity demanded; the extra credit problem gives you information to determine the slope for a light drinker and the slope for a heavy drinker.

1.When the term "price" is used in the law of demand, price refers to Select one:

a. the price of the well relative to the price of another good.

b. the nominal price of the well relative to its nominal price in the previous year.

c. the absolute price of the good.

d. the dollar price of the good.

2.In economics, the meaning of demand refers to Select one:

a. the quantities of a good that people will sell at various prices.

b. the total satisfaction that consuming good provides people at different prices.

c. how badly someone wants a good.

d. the quantities of a good that people will buy at various prices.

3.Which of the following illustrates the law of demand?

Select one:

a. College enrollment increases when federal tuition grants are readily available to students.

b. More people watch college basketball in March than in November.

c. The number of long-distance calls in the United States is greater on Christmas than on Valentine's Day.

d. The prevailing wage rate in an industry determines how many people choose to work in the industry.

4.The absolute price of a good is its

Select one:

a. money price.

b. projected price.

c. relative price.

d. subjective price.

5.The only variable that can affect a movement along the demand curve is

Select one:

a. the number of buyers.

b. income levels.

c. the price of the good itself.

d. the number of substitutes.

6.The price of an MP3 music player increased from $50 to $70 while the price of a music download increased from $1 to $2. The relative price of an MP3 music player in terms of music downloads Select one:

a. increased from 0.04 to 0.05.

b. decreased, but we need more information to know by how much.

c. increased, but we need more information to know by how much.

d. decreased from 50 to 35.

7.The quantity supplied of a particular good is the amount of the good that

Select one:

a. households want firms to sell at each price during a particular time period.

b. firms will actually end up buying at a particular price during a given time period.

c. firms are willing to sell at each price during a particular time period.

d. households are willing to consume at each particular price.

8.An increase in price will lead to an increase in quantity supplied. This statement is

Select one:

a. the law of supply.

b. untrue always.

c. the law of demand.

d. a normative statement.

9.Regarding the law of supply, which of the following statements is correct?

Select one:

a. As demand falls, supply rises.

b. The ceteris paribus assumption does not apply.

c. As the price of a good or service rises, the quantity supplied will increase.

d. As the price of a good or service rises, the quantity supplied will decrease.

10.A given supply curve illustrates Select one:

a. the relationship between expected future prices and quantity supplied.

b. the effect of a change in resource costs on the quantity supplied.

c. the effect of a change in technology on the quantity supplied.

d. the relationship between price and quantity supplied.

11.If there is a decline in the price of milk, an input in the production of ice cream, then there will be a(n)

Select one:

a. decrease in the supply of ice cream and a leftward shift of the supply curve.

b. increase in the supply of ice cream and a rightward shift of the supply curve.

c. increase in the quantity of ice cream supplied and a movement down along the supply curve.

d. decrease in the quantity of ice cream supplied and a movement up along the supply curve.

12. An improvement in technology in the production of computers would

Select one:

a. increase the demand for computers.

b. decrease the supply of computers.

c. decrease the demand for computers.

d. increase the supply of computers.

13.Which of the following is a non-price determinant of supply? Select one:

a. the number of consumers

b. technological advances in production

c. the price of related goods consumers may buy

d. consumers' incomes

14.Which of the following does NOT cause a rightward shift in the supply curve?

Select one:

a. a reduction in resource costs

b. an increase in technology

c. a reduction in the expected future price of the good

d. a reduction in the price of the good

15.Which of the following is a possible outcome of setting a legal maximum rental rate below the market-clearing rental rate?

Select one:

a. a decrease in the quantity of rental housing demanded

b. an increase in the quantity of rental housing supply

c. a black market in rental housing

d. a surplus of rental housing

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