Initial Publication Date: April 12, 2016
Variables and Parameters: Sample Problems
Problem 1:
The graph below shows the surfboard supply market:
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Provenance: Peter Schuhmann, University of North Carolina-Wilmington
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- Which pieces of information are variables?
- Which pieces of information are parameters?
- How does the parameter describe the relationship between the variables?
- Price and Quantity supplied are variables in this model because they vary.
- The slope of the supply function is a parameter in this model because this value summarizes the relationship between price and quantity supplied for the entire group of sellers.
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The slope is 0.5:
$\text{rise}/\text{run} = (\$600 - \$400) / (1400 - 1000) = 200/400 = 0.5$
This shows that the relationship is positive: quantity supplied rises as price increases.
The relationship is also linear, a straight line.
Problem 2:
The graph below shows changes in household savings when income changes:
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- Which pieces of information are variables?
- Which pieces of information is a parameters?
- How does the parameter describe the relationship between the variables?
- Savings and income are variables in this model because they vary.
- The slope and the intercept on vertical axis are parameters in this model because they show how much savings changes as income changes (the slope) and how much saving we can expect if incomes are zero (a negative savings where the line intersects the vertical axis at savings = 0).
- The slope (0.9) shows the relationship is positive and it is linear, a straight line.
Problem 3:
The graph below shows the change in loanable funds when interest rates change:
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- Which pieces of information are variables?
- Which pieces of information is a parameters?
- How does the parameter describe the relationship between the variables?
- Quantity of loanable funds and the interest rate are variables in this model because they vary.
- The slope is a parameter in this model because it shows how much loanable funds change when the interest rates changes.
- The slope (-1/10) shows the relationship is negative and it is linear, a straight line.
Problem 4:
The graph below shows the change in the demand for money when the interest rates change:
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- Which pieces of information are variables?
- Which pieces of information is a parameters?
- How does the parameter describe the relationship between the variables?
- Quantity of money demanded and the interest rate are variables in this model because they vary.
- The slope is a parameter in this model because it shows how much the demand for money changes when the interest rates changes.
- The slope (-1/10) shows the relationship is negative and it is non-linear, not a straight line.
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