Kyra buys an iPhone for \(240\)dollar and gets consumer surplus of \(160\)dollar. a. What is her willingness to pay? b. If she had bought the iPhone on sale for \(180\)dollar, what would her consumer surplus have been? c. If the price of an iPhone were \(500\)dollar, what would her consumer surplus have been?

Understanding the concept of 'willingness to pay' is essential for both consumers and producers as it defines the maximum amount an individual is willing to spend for a product or service. It reflects the value a consumer places on a good, based on personal preferences, income, and utility derived from the product.

Take Kyra as an example. She buys an iPhone for \(240\) and gains a consumer surplus of \(160\). Her consumer surplus is the difference between her 'willingness to pay' and the actual price paid. Consequently, her 'willingness to pay' is the sum of these two values, thus \(400\).

This amount is significant because it indicates the highest price Kyra is comfortable with before she refrains from purchasing. If the price exceeds her 'willingness to pay', Kyra will likely avoid buying the iPhone, as seen when the hypothetical price is set to \(500\).

The 'economic value' of a good or service is inherently linked to a consumer's 'willingness to pay.' It represents the total benefit a consumer gets, including both the usage of the product and the monetary value of the satisfaction derived from it. The 'willingness to pay,' therefore, can be seen as a direct measure of this 'economic value.'

For instance, Kyra's assessment of the iPhone's 'economic value' is above \(240\), as she experiences a consumer surplus, illustrating that she receives more value than the monetary cost. Her perceived 'economic value' is high enough to warrant a \(160\) consumer surplus at the actual purchase price.

When Kyra encounters a sale price of \(180\), her consumer surplus increases to \(220\), indicating a considerable gain in economic benefit due to the reduced cost. This highlights how the 'economic value' Kyra places on the iPhone significantly exceeds the market prices discussed in the exercise.

The 'price elasticity of demand' is a measure indicating how much the quantity demanded of a good changes in response to a change in price. Highly elastic demand means that consumers will significantly alter their quantity demanded with minor price changes. Conversely, inelastic demand implies little to no change in quantity demanded with price fluctuations.

Kyra's situation can be used to explain 'price elasticity of demand' for iPhones. If Kyra, like many consumers, has a high 'willingness to pay' for the iPhone, it suggests a potentially inelastic demand. Essentially, even if the price increases, Kyra and others might continue purchasing iPhones up to a certain price point—an indicator of strong brand loyalty and high perceived value.

However, a price increase to \(500\) results in a negative consumer surplus for Kyra, demonstrating a threshold where demand becomes elastic. Kyra's demand for iPhones reacts to the price increase, and in this case, exceeds her 'willingness to pay,' signaling that she would decrease her quantity demanded to zero because the price surpasses her perceived value.