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Chapter 6: Problem 5

Suppose that 1,000 people in a market each have the same monthly demand curve for bottled water, given by the equation \(Q^{D}=100-25 P\), where \(P\) is the price for a 12 -ounce bottle in dollars. a. How many bottles would be demanded in the entire market if the price is \(\$ 1 ?\) b. How many bottles would be demanded in the entire market if the price is \(\$ 2 ?\) c. Provide an equation for the market demand curve, showing how the market quantity demanded by all 1,000 consumers depends on the price.

Short Answer

Expert verified
a. 75,000 bottles would be demanded in the entire market if the price is $1. b. 50,000 bottles would be demanded in the entire market if the price is $2. c. The market demand curve equation is \(Q^{D}_{market} = 1000 * (100-25 P)\).

Step by step solution

01

Determine the quantity demanded when the price is $1

To do this, substitute \(P = 1\) into the individual demand equation \(Q^{D}=100-25 P,\) which leads to \(Q^{D}=100-25*1 = 75\). This means each consumer would demand 75 bottles.
02

Multiply the individual demand by the total number of consumers

There are 1000 consumers in the market. By multiplying the per-consumer demand by the total number of consumers, we get the total market demand: \(1000 * 75 = 75,000\). So, 75,000 bottles would be demanded in the entire market when the price is $1.
03

Determine the quantity demanded when the price is $2

Do the same as in step 1 but this time, substitute \(P = 2\) into the equation \(Q^{D}=100-25 P,\) which results in \(Q^{D}=100-25*2 = 50\). Hence, each consumer demands 50 bottles at a price of $2 per bottle.
04

Multiply the individual demand by the total number of consumers for price $2

Analogous to step 2, multiply the per consumer demand by the total number of consumers to get market demand at price $2: \(1000 * 50 = 50,000\). Therefore, 50,000 bottles would be demanded in the entire market when the price is $2.
05

Provide an equation for the market demand curve

The market demand is calculated by multiplying the individual demand by the total number of consumers. Therefore, the market demand equation is \(Q^{D}_{market} = 1000 * (100-25 P)\). This equation shows how the market quantity demanded by all 1000 consumers depends on the price.

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Most popular questions from this chapter

When an economy is experiencing inflation, the prices of most goods and services are rising but at different rates. Imagine a simpler inflationary situation in which all prices, and all wages and incomes, are rising at the same rate, say 5 percent per year. What would happen to consumer choices in such a situation? (Hint: Think about what would happen to the budget line.)

[Uses the Indifference Curve Approach] With the quantity of popcorn on the vertical axis and the quantity of ice cream on the horizontal axis, draw indifference maps to illustrate each of the following situations. (Hint: Each will look different from the indifference maps in the appendix, because each violates one of the assumptions we made there.) a. Larry's marginal rate of substitution between ice cream and popcorn remains constant, no matter how much of each good he consumes. b. Heather loves ice cream but hates popcorn.

What would happen to the market demand curve for polyester suits, an inferior good, if consumers' incomes rose?

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[Uses the Indifference Curve Approach \(]\) The appendix to this chapter states that when a consumer is buying the optimal combination of two goods \(x\) and \(y,\) then \(M R S_{y, x}=P_{x} / P_{y^{*}}\) Draw a graph, with an indifference curve and a budget line, and with the quantity of \(y\) on the vertical axis, to illustrate the case where the consumer is buying a combination on his budget line for which \(M R S_{x x}>P_{x} / P_{y}\).
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