SAT College

Given the following two functions. Qa=50+p. Qb=200-4p. (A) IDENTIFY WHICH IS THE SUPPLY FUNCTION OF DEMAND FUNCTION
(B) WHAT IS THE IS EQUILIBRIUM PRICE OF THE QUANTITY
(C) WHAT IS THE PRICE ELASTICITY OF SUPPLY FOR THIS

Answers

Answer 1
(A) The supply function generally is considered to have positive slope. Qa has positive slope. Qb has negative slope, so is probably the demand function.
  supply function: Qa
  demand function: Qb

(B) The equilibrium price is the price that makes supply equal to demand.
  Qa = Qb
  50 +p = 200 -4p
  5p = 150
  p = 30
The equilibrium price is 30.

(C) The price elasticity of supply is computed as
  Es = (dQa/dp)·(P/Qa) = 1·p/(50+p)
  Es = p/(50+p)

At p=30, the numerical value is Es = 30/80 = 3/8. Qualitatively, the supply is inelastic.
Answer 2

Answer:

B - 30
C - 0.412

Explanation:

A) Qa=50+p is the supply function and Qb=200-4p is the demand function.

(B) The equilibrium price is the price at which the quantity demanded is equal to the quantity supplied. We can find the equilibrium price by setting Qa equal to Qb and solving for p:

Qa = Qb

50 + p = 200 - 4p

5p = 150

p = 30

Therefore, the equilibrium price is 30.

(C) The price elasticity of supply is a measure of how responsive the quantity supplied is to changes in price. We can calculate the price elasticity of supply using the following formula:

Price elasticity of supply = (percent change in quantity supplied) / (percent change in price)

To find the price elasticity of supply for this case, we can first find the slope of the supply function Qa=50+p. The slope of the supply function is 1, because for every 1 unit increase in price (p), the quantity supplied (Qa) increases by 1 unit.

Next, we can use the midpoint method to find the percent change in quantity supplied and the percent change in price. Let's say the initial price is 30 and the initial quantity supplied is 80 (Qa=50+30). If the price increases to 40, the quantity supplied increases to 90 (Qa=50+40).

The percent change in quantity supplied is (90-80)/((80+90)/2) = 10/85 = 0.118

The percent change in price is (40-30)/((30+40)/2) = 10/35 = 0.286

Substituting these values into the formula above, we get:

Price elasticity of supply = 0.118 / 0.286 = 0.412

Therefore, the price elasticity of supply for this case is 0.412. This means that for every 1% increase in price, the quantity supplied increases by 0.412%.

Related Questions

Which of the five measures of center (the mean, the median, the trimmed mean, the weighted mean, and the mode) can be calculated for quantitative data only.

Answers

In Chapter 2 we discussed how to summarize data using different methods and to display data using graphs. Graphs are one important component of statistics; however it is also important to numerically describe the main characteristics of a data set. The numerical summary measures, such as the ones that identify the center and spread of a distribution, identify many important features of a distribution. For example, the techniques learned in Chapter 2 can help us graph data on family incomes. However, if we want to know the income of a “typical” family (given by the center of the distribution), the spread of the distribution of incomes, or the relative position of a family with a particular income, the numerical summary measures can provide more detailed information (see Figure 3.1). The measures that we discuss in this chapter include measures of (1) central tendency, (2) dispersion (or spread), and (3) position.
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Each of these five measures of center 1) the mean, 2) the median, 3)the trimmed mean, 4) the weighted mean, and 5) the mode can be measured and written down in number. Thus, they are all quantitative data. 


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Answers

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