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Economics Homework Ten - Model (view source)
Revision as of 03:35, March 5, 2011
, 03:35, March 5, 2011no edit summary
:::P<sub>ed</sub>=((Q<sub>2</sub>-Q<sub>1</sub>)/Q<sub>1</sub>)/((P<sub>2</sub>-P<sub>1</sub>)/P<sub>1</sub>)
:::P<sub>ed</sub>=((Q<sub>2</sub>-Q<sub>1</sub>)/Q<sub>1</sub>)/((P<sub>2</sub>-P<sub>1</sub>)/P<sub>1</sub>)
::But the above formula is simply an approximation, and the higher precision provided by calculus is needed to prove this rigorously. So we rewrite the above equation using calculus:
::But the above formula is simply an approximation, and the higher precision provided by calculus is needed to prove this rigorously. So we rewrite the above equation using calculus, such that P<sub>ed</sub> equals:
:::<math>P<sub>ed</sub>=\frac{dQ}{dP}{1/Q<sub>1</sub>}{1/P<sub>1</sub>}</math>
:::<math>\frac{dQ}{dP}X\frac{1/Q}{1/P}</math>
::where you can think of "dQ" as replacing a tiny change in Q (i.e., Q<sub>2</sub>-Q<sub>1</sub>) and "dP" replacing a tiny change in P (i.e., P<sub>2</sub>-P<sub>1</sub>) in the above equations. "dQ/dP" is the "differential" of Q with respect to P (i.e., the tiny change in Q based on a tiny change in P).
::We can now solve the differential equation for P<sub>ed</sub> by substituting in Q=30/P:
:::<math>\frac{d}{dP}\frac{30}{P}X\frac{1/Q}{1/P}</math>
::differentiating in the first half and substituting P=30/Q in the second half yields:
:::<math>\frac{-30}{P^2}X\frac{30}{Q^2}</math>
::substituting in Q=30/P and P=30/Q yields:
:::<math>\frac{-Q}{P}X\frac{P}{Q}</math>
and thus P<sub>ed</sub>= -1. By convention, because price elasticity of demand for one good is always negative, the negative sign is dropped and we have our answer: price elasticity is 1. (Price cross-elasticity of demand may be positive or negative, depending on whether the two goods are substitutes or complements.)
9. Provide, in your own words, the best definition of "public good" that you can.
9. Provide, in your own words, the best definition of "public good" that you can.
:The correct answer is shortage of 600. A shortage occurs because a price ceiling increases demand, without adjusting output- in fact, output will ... decrease, because producers are now making less money. Specifically, the shortage can be measured by measuring the quantity between where a line representing the price ceiling intersects the supply curve and demand curve. (Addison)
:The correct answer is shortage of 600. A shortage occurs because a price ceiling increases demand, without adjusting output- in fact, output will ... decrease, because producers are now making less money. Specifically, the shortage can be measured by measuring the quantity between where a line representing the price ceiling intersects the supply curve and demand curve. (Addison)
[[Category:Economics lectures]]