A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
A consumer has utility (see image) on ice creams (x) and cakes (y).
(a) Are the indifference
(b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x).
(c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
![**Equation:**
The expression provided is a mathematical function of two variables, x and y. It is denoted as:
\[ u(x, y) = 2\sqrt{x} + \sqrt{y} \]
**Explanation:**
This function, \( u(x, y) \), is composed of square root terms. The expression represents a surface in three-dimensional space where \( u \) is the function of \( x \) and \( y \). For any set of \( x \) and \( y \) values, the function calculates the corresponding \( u \) value as described.
- \( 2\sqrt{x} \): This term involves the square root of \( x \) multiplied by 2.
- \( \sqrt{y} \): This term involves the square root of \( y \).
The combination of these terms indicates how the value of \( u \) changes based on changes in \( x \) and \( y \). This type of function might be used in various fields, such as physics or engineering, to model phenomena involving spatial variables.
**Visual Representation:**
If a graph were to be included, it would be a surface plot representing the function \( u(x, y) \) over a range of \( x \) and \( y \) values. The surface would illustrate how \( u \) increases as either \( x \) or \( y \) increases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30841e31-469e-444c-92f7-f4f3d21a3fe0%2Ff345bbea-b242-403b-b631-75a7a602cf12%2Facs9ovd_processed.jpeg&w=3840&q=75)
Utility: It can be defined as the wants satisfying power of a good. In simple words, utility is the power that a good or service possesses to meet and satisfy human wants.
Demand function: The demand function describes the functional inverse relationship that exists between the price and the quantity demanded of a commodity.
Normal goods: A good is considered a normal good if there is a positive relationship between the income of the consumer and the demand for the good, i.e., with the rise in the income of the consumer, the demand for the good also rises, and vice versa.
Substitute good: Two goods are said to be substitute goods if the rise in the price of one causes a rise in the demand for another, and vice versa.
Complementary goods: Two goods are said to be complementary goods or complement when the rise in the price of one good causes a fall in the demand for another good, and vice versa.
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