Demand: E-Readers The demand for Amazon's Kindle e-reader...

Demand: E-Readers The demand for Amazon's Kindle e-reader can be approximated by $q=\frac{760}{p}-1$ million units per year $(60 \leq p \leq 400)$ where $p$ is the price charged by Amazon. $^{31}$ Assume that Amazon is prepared to supply $q=0.019 p-1$ million units per year $\quad(60 \leq p \leq 400)$ at a price of $$\$ p$$ per unit. a. Calculate the equilibrium price and equilibrium demand. b. $T$ Graph the demand and supply functions to confirm your answer in part (a) graphically. c. Estimate, to the nearest 0.1 million units, the surplus or shortage of Kindle e-readers if the price is set at $\$ 72$

Demand: E-Readers The demand for Amazon's Kindle e-reader can be approximated by
$q=\frac{760}{p}-1$ million units per year $(60 \leq p \leq 400)$
where $p$ is the price charged by Amazon. $^{31}$ Assume that Amazon is prepared to supply
$q=0.019 p-1$ million units per year $\quad(60 \leq p \leq 400)$
at a price of $$\$ p$$ per unit.
a. Calculate the equilibrium price and equilibrium demand.
b. $T$ Graph the demand and supply functions to confirm your answer in part (a) graphically.
c. Estimate, to the nearest 0.1 million units, the surplus or shortage of Kindle e-readers if the price is set at $\$ 72$

Key Concepts

Graphical Analysis

Graphical analysis in economics involves plotting the demand and supply curves on a graph, which helps visualize the relationship between price and quantity. The point where the two curves intersect represents the market equilibrium. This visual representation aids in confirming analytical results, illustrating concepts like surpluses (when supply exceeds demand) or shortages (when demand exceeds supply) under different pricing scenarios.

Surplus and Shortage

A surplus occurs when the quantity supplied exceeds the quantity demanded at a given price, leading to downward pressure on prices. Conversely, a shortage happens when the quantity demanded is greater than the quantity supplied, typically causing prices to rise. In practical applications, calculating the surplus or shortage at non-equilibrium prices helps analyze market imbalances and informs decisions regarding price adjustments or policy interventions.

Supply Function

The supply function describes the relationship between the price of a good and the quantity supplied by producers. Typically, this function has a positive slope, reflecting that higher prices incentivize producers to supply more of the good. It is essential for analyzing how producers react to changes in market prices and for determining the quantity available in the market at different price levels.

Market Equilibrium

Market equilibrium is the state where the quantity of goods demanded by consumers equals the quantity of goods supplied by producers. At this point, the market clears, meaning there is neither a surplus nor a shortage. In economic analysis, determining the equilibrium involves solving the equation where the demand function equals the supply function, resulting in the equilibrium price and corresponding equilibrium quantity.

Demand Function

The demand function represents the relationship between the price of a good and the quantity demanded by consumers. It generally has a negative slope, indicating that as the price increases, the quantity demanded decreases, and vice versa. This function is fundamental in understanding consumer behavior and predicting changes in market demand in response to price changes.

Transcript

00:01 For this problem, we are told that the demand for amazon's kindle e -reader can be approximated by q equals 760 over p minus 1 million units per year, where p is the price charged by amazon.

00:13 And we are to assume that amazon is prepared to supply q equals 0 .019p minus 1 million units per year at a price of p dollars per unit.

00:21 For part a, we are asked to calculate the equilibrium price and equilibrium demand.

00:26 So we have qd equals 760p minus 1 and qs equals 0 .019p minus 1.

00:39 So what we want is qd to equal qs.

00:43 So we set 700, let's see here, 760 over p minus 1 to equal 0 .019 p minus 1.

00:53 Can add one to both sides to isolate those terms of p, then multiply through by p to get p, or multiply through by p and divide by 0 .019 to get p squared equal 760 over 0 .019.

01:10 So the absolute value of p is going to be the square root of 760 over 0 .019, which then indicates that if we calculate that out, we find that the absolute value of p is going to be the square root of 760 over 0 .019, which then indicates that, value of p is going to equal 200, but we're told that p is going to be between 60 and 400, which tells us that we have one meaningful root at p equals 200.

01:35 So for part b, we are asked to graph the demand and supply functions to confirm the answer in part a graphically.

01:42 So here we have the crossover point between the two lines.

01:47 You can see that it is at a price of 200 and at a demand or a support...

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